With no party predicted to win outright in May, Britain is expected to face one of four outcomes – all of which will require coalition or negotiation that will test the parties’ leadership.

1. Conservative minority government

If Labour loses as much in Scotland as it could gain in England, and the Conservatives snap up a few handy gains from their Liberal Democrat partners, on election night 2015 – just as in 2010 – the only durable government would be headed by the Tories. But with David Cameron having failed for a second time to secure for his party the overall majority that it still imagines to be its entitlement, the PM can only cling on to the party leadership into a second term by demonstrating that he can do things differently, which means cutting the rump Lib Dems loose and seeking to govern alone.

The most immediate challenge is charting a path through a mostly-hostile House of Commons for a Queen’s speech and, a little later, a budget. Not far behind is getting the 2017 in/out referendum on Europe agreed. Cameron long ago made this a personal “red line” for remaining in office, and his party will not let him forget it.

The players

In scrambling together the vote-by-vote parliamentary alliance he needs to survive, Cameron may well turn first to the unionists of Northern Ireland. The Ulster Unionist party has close historic ties with the Tories. The harder-line Democratic Unionists will certainly be there, with Westminster leader Nigel Dodds the man making deals on the ground, with the DUP’s founding member, leader and first minister, Peter Robinson, an influence in the background.

Even if Ukip has a so-so election, the former Tory Douglas Carswell can expect to hold Clacton, and will be one obvious person to do business with. If it does much better, the party could have 10 or more MPs, including Nigel Farage who is set to run in South Thanet. But if the Tories fall substantially short of the magic 326 seats that give a majority, they are likely to need to go back to the Lib Dems too. It might be that Nick Clegg is still the man to talk to, but even if the students of Sheffield Hallam don’t give him the boot, his own party might; in which case, it might be necessary to cut a deal with a more instinctively anti-Conservative leader, such as Tim Farron or Vince Cable.

The deals

The Democratic Unionists would bargain hard – and in the traditional hard currency of financial privileges for the province. Northern Ireland faces perennial public spending pressures which would surely come into play, but so too would its hopes of setting its own corporation tax rate, to try to woo business away from the Republic, where the rate is just 12.5%. London has made sympathetic noises, but is currently buying time in negotiations, not least because it fears emboldening Scottish nationalists who are demanding the same freedom. But if unionist votes were needed to get a Queen’s speech through, demands for devolution on corporation and almost anything else could soon be agreed.

For Ukip, Nigel Farage has made plain that the first and most important issue would be that EU referendum. His party would want it brought forward – probably to autumn 2015 – and might insist that Cameron commit to giving Eurosceptic ministers the freedom to campaign for an out vote, or even attempt to bind him into campaigning for that himself.

A second coalition with the Tories could shatter an already-demoralised and shrunken Liberal Democrat party. It would need something substantial and bankable in return, not subject to a referendum like Clegg’s disastrous plebiscite on the alternative vote. An immediate commitment to proportional representation in local government would be an obvious example.

2. Labour minority government

Working-class Tories have always had doubts about Cameron, and in 2015 they could desert him in droves. Right around the southern English coast, and through pinched Midlands suburbs, Ukip could take enough votes to knock the Conservatives out of contention, but rarely enough to win. There might be little enthusiasm for Ed Miliband, but after five years of austerity the chance to “get the Tories out” could be enough to bring Labour voters home, and to stem the feared blood-letting in Scotland.

Labour would fall short of the winning line, but Miliband’s Commons bloc could still be the biggest. But how will he get to No 10? He might fancy a nice stable deal with the Lib Dems, but having lacked the popularity to win the election outright, Miliband would lack the authority within his own tribe to stitch one together. Disraeli wrote that England did not love coalitions, but Labour – which has never forgotten the betrayal of National Government in 1931 – positively despises them. He is condemned to survive by continuous haggling in a minority government.

The players

The most straightforward first call would be to Alasdair McDonnell, leader of Norther Ireland’s SDLP, which has historically regarded itself as Labour’s sister party. If the Greens have a good election, Caroline Lucas will be back in Brighton, together with one or two new colleagues, although almost certainly not party leader Natalie Bennett, who is contesting a rock-solid Labour seat at Holborn and St Pancras. That likely leaves Lucas in charge of negotiating with Miliband.

The scale of Lib Dem losses would most likely prompt Clegg to resign immediately. Vince Cable could take over, paving the way for deals with Labour.

On the nationalist benches, Elfyn Llwyd of Plaid Cymru and Angus Robertson of the SNP are the notional Westminster leaders, but with Alex Salmond newly-returned for Gordon, few are under any illusions that bigger players are not also involved.

The deals

From Holyrood, first minister and new SNP leader Nicola Strugeon has suggested that non-renewal of Trident could be a deal-breaker for her party, and – in this scenario – her call could resonate with several of the other votes that Miliband would need to buy. Both Plaid and the Greens are firmly against nuclear weapons, and for the Lib Dems in some moods, too, opposition to Trident has been a badge of radicalism. In 2010, they stood against like-for-like replacement of the submarines, a policy that has since got lost in reviews. But diminished in strength and desperately seeking to differentiate themselves from their erstwhile coalition partners in 2015, they could go further and call for Trident to go entirely – and then push a reluctant Labour leadership to do the same.

Many Labour MPs and activists might be happy with this disarming outcome from this informal “rainbow coalition”, as they would also be if the nationlists and the Greens could persuade Labour to ease up on the pace of austerity. But on both defence and the economy, where Miliband is painfully sensitive to being caricatured as an old-fashioned left-winger, he will be especially reluctant to be seen to be allowing to the political fringes to dictate the agenda, so he will seek to minimise the concessions.

3. Lib Dems as kingmakers again

The Lib Dems could lose half their seats and still be the deciding factor in the next government. If the two big parties are more or less tied on two-hundred and eighty-something a piece, then although somewhat reduced, the Lib Dem parliamentary tribe is more powerful than ever – with a free hand to pick the prime minister.

The players

Although he avoided outright oblivion, Nick Clegg now follows a fairly disappointing election in 2010 with a considerable loss of both votes and seats, which makes survival a challenge. Miliband has a decision to make: whether or not to call for Clegg to go, on the basis that his past relationship with Cameron precludes him approaching his rival prospective partners in an even-handed way. The Labour tribe would expect this, but it could have the perverse effect of rallying Lib Dem loyalists to Clegg.

Should Clegg wish to hang on, and succeed, his twin priorities would be reaffirming the virtues of coalition in general, and justifying his post-2010 record in particular. The former would point to entering serious negotiations with Labour, but the latter would ultimately curtail his flexibility towards Miliband, especially in relation to austerity. All this would make a fresh deal with the Tories more likely.

But should Clegg go, the obvious replacements – Tim Farron or Vince Cable – would probably regard it as their mission to disentangle the struggling party from the Tories, and some sort of accommodation with Labour becomes more likely, although it may be that the instinctively oppositional Farron, in particular, would prefer an informal arrangement to back Miliband in passing a budget, rather than another exhausting coalition.

The deals

If Clegg survives and is cutting deals with Cameron again, he would want cast-iron guarantees on the constitutional reforms he feels he was cheated of last time: a specific plan and timetable for Lords reform in place of the warm words of 2010, PR for local government elections and, perhaps, major new powers for councils. He would also push for more money on his other pet projects: the pupil premium in education, and a higher personal tax allowance, which he might this time take care to prevent the Tories extending to higher-rate taxpayers. The wildcard could be the EU referendum, which Cameron is committed to, and Clegg hasn’t ruled out, but parts of his party may recoil from.

If Farron or particularly Cable were dealing with Labour, they might try to push specific “invest to grow” public spending propositions within a still generally austere fiscal framework, as well as progressive tax rises. But they would also demand reassurances on civil liberties, in particular a guarantee that there would be no attempt to reinvigorate the “snooper’s charter”, as well as constitutional commitments on things like reforming the Lords. A cash-strapped party relieved to have survived one election may also be concerned to see that there will be no early amendment to – or manoeuvring around – the fixed-term parliament act.

4. The SNP grab the whip hand

The SNP post-referendum march could see it taking 40-plus of Westminster’s 59 seats. The bulk of this gain would be, of course, at Labour’s expense, but elsewhere in the UK it fared reasonably well, picking up 40-odd seats from a Ukip-sapped Tory party in England and Wales, which left the two parties tied. The Lib Dems, meanwhile, had an even worse night than everyone had predicted – losing substantially to the SNP, Labour and the Conservatives, to return to Westminster with just shy of 20 seats, far too few to push either big party across the winning line.

The players 

Angus Robertson may be the SNP’s notional Westminster leader, but after this sort of transformative result, it is plainly not up to him, but to the SNP’s biggest beasts to decide how to play their cards, specifically first minister Nicola Sturgeon, and the newly-elected MP for Gordon, Alex Salmond. Despite his profile and his presence in the Commons, Sturgeon counts for more, because as party leader she wields all the patronage, and – just as importantly – is unencumbered by his personal promise not to seek another referendum.

The arithmetic now dictates that nobody can govern without SNP acquiescence, which rules out the Tories, whom they had pre-committed to keeping out of power. But though all-conquering in Scotland, the SNP is still not quite big enough to give Labour a stable working majority, so Plaid Cymru, Northern Irish MPs and the rump Lib Dems could all be part of the discussion if there were serious efforts to build an enduring coalition. But will there be any such efforts? The Nationalists, who now have the votes to break any plausible government in Westminster, may have many priorities, but it should not be assumed that the stability of government in London is one.

The deals

Although the SNP has talked about Trident and protecting parts of public spending, after its landslide win, the party’s expanded and excited base expects an early return to Scotland’s constitutional future, and Sturgeon does not disappoint. Rapidly, she points out that it was Salmond and not she who said he would never fight another referendum, and gives a major speech suggesting that – after the “betrayal” of the Smith commission on devolution – the general election makes plain that 2014’s no vote cannot be regarded as Scotland’s final word. Specifically, she might demand immediate “home rule” over all taxes and social security, while also seeking to exert a pull on reserved matters such as defence and demanding legislation for some form of referendum a few years down the road.

All the traditional, UK-wide parties retain their notional unionism, but there are growing doubts about whether the Nationlist tide can any longer be turned. And Labour, suddenly so diminished in Scotland, no longer has the same partisan reason for regarding national divorce as so unconscionable that it would rather stay out of power than talk turkey with the SNP