What are the constitutional options?

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*Is there a constitutional basis behind the demands for Gordon Brown to resign immediately?

No. Under Britain's (unwritten) constitution the incumbent at No. 10 is expected to stay on as a caretaker prime minister to deal with pressing matters of state until a new Government can be formed.

As Gerry Stoker, the Professor of politics and governance at the University of Southampton, said: "The coverage criticising Mr Brown for not resigning is wide of the mark. If he went and tendered his resignation the Queen would say to him 'you can't do it, because there's no alternative'."

What types of deals could the Tories and Lib Dems do to form a new government?

There are three main types of deal the Conservatives and Liberal Democrats could do. Firstly enter into a full coalition, including cabinet positions for prominent Liberal Democrats and a shared legislative agenda. Secondly a "confidence and supply agreement", by which the Tories could exchange policies for the Liberal Democrats' promise not to vote against the government on specific votes of confidence. In return, the Liberal Democrats would receive some ministerial positions and a share of the legislative agenda in the Queen's Speech. They would also have the option to "agree to disagree" with the government on aspects of policy, maintaining their independent identity. The third option would be a minimal version of "confidence and supply", whereby the Liberal Democrats would abstain from voting against major supply measures or confidence votes and agree on a broad trajectory of fiscal consolidation. They would maintain more independence, but receive limited concessions and a minor say in the Queen's Speech and Budget.

Does Mr Cameron need to get the support of his MPs to do a deal with the Liberal Democrats as Clegg has to?

Unlike the Liberal Democrats, which have to secure the support of three-quarters of both their MPs and the Federal Executive to enter into a coalition, David Cameron's Conservatives have no such restrictions. However, Mr Cameron will be bound by political realities, and will have to take into account the views of powerful interest groups such as the 1922 Committee of backbench MPs as well as grassroots activists.

Could the Nationalists, Liberal Democrats and Labour come together to propose legislation under a minority Tory government?

This prospect is entirely possible, but unlikely as the government sets the Commons' agenda and would ensure it was tightly controlled.

"The standing orders of Parliament are very government-driven; they control the timetable," said Philip Cowley, the professor of parliamentary government at the University of Nottingham. "The opposition parties would have to introduce legislation as private members. But they can amend or defeat bits of government legislation and that is the only real power they would have."

What would precipitate another general election?

The tests for the viability of a government are the results of "confidence and supply" motions. If the government loses one of these, they must return to the country and hold another election seeking a majority of seats.

The first example of such a vote is after the Queen's Speech, in which the prime minister outlines his new government's broad legislative agenda. It is scheduled for 25 May. The supply vote rule is fluid and complex, said Professor Cowley, and acutely sensitive to the language used in a motion: "There are two ways a vote of confidence can trigger a general election: one is if it's a motion that contains the word 'confidence' – as in 'this House has no confidence in Her Majesty's Government' – or if it is a vote on a piece of legislation which the government has itself declared to be a vote of confidence and the rest of the House understands it as such," he said.

"Therefore, the government can lose a vote on the budget, that doesn't precipitate an election in and of itself. A defeat on the Queen's Speech would, as would a defeat on a piece of legislation the Conservatives had been declared to be a vote of confidence."

Often governments play brinksmanship, declaring a vote one of 'confidence' in order to force it through. Obviously, the downside of this tactic is that if they are defeated it triggers an immediate election.

"Around all of the legal framework are political realities," said Professor Cowley of this situation. "The brutal reality at the moment is that whatever they say, frankly none of them want another general election, not least because none of them can afford another election. And that's particularly true of the Lib Dems and Labour, but also the Tories."

Could the Liberal Democrats pull out of a deal with the Tories in a year or so to form a Lab-Lib pact without an election?

There is nothing to stop any party in a coalition from abandoning any form of alliance at any point – but this would almost certainly lead to a new election.

The minority government left behind would have two options: go to the palace and seek a dissolution from the monarch, or try to carry on. However if they lost a "confidence and supply" they would have no choice but to call fresh elections.