The answer to the first question is that, although Mr Prescott would still be deputy leader, so far Mr Blair has refused to say that he would be Deputy Prime Minister - despite the fact that he shadows Michael Heseltine, for whom the title was revived last year.
The Independent understands that Mr Blair has promised Mr Prescott the title First Secretary, an office held by George Brown and Barbara Castle in Harold Wilson's first administration. The assumption must be that Mr Prescott would deputise for Prime Minister Blair in the Commons.
But Mr Prescott would not automatically become Prime Minister if, in the delicate language of the Labour Party constitution, Mr Blair became "permanently unavailable".
A rule change made at the 1993 Labour conference says that, in government, the Cabinet must choose one of its number to be Acting Prime Minister until a new leader is elected. On the basis of the present Shadow Cabinet, that would seem to be a close race between Chancellor Gordon Brown and Foreign Secretary Robin Cook.
Labour governments have not had a Deputy Prime Minister since the title was held by Herbert Morrison in 1945-51. But Harold Wilson had a First Secretary, throughout his 1964-70 government, who ranked second in the ministerial pecking order. The title was invented, after the "night of the long knives" in 1962, for RA Butler - who also combined it with Deputy Prime Minister.
It is believed that Mr Blair has not yet made a decision about Mr Prescott's departmental responsibilities if Labour wins the next election. Press reports that he might be made Home Secretary are met with standard dismissals of "pure speculation" from Labour officials.
Some Labour MPs assume the Home Office is regarded as a "safe" job which would keep him occupied, and well away from shadow Chancellor Gordon Brown's economic responsibilities. It also has the advantage, according to one observer, that Mr Blair, as a former shadow Home Secretary, would be able to keep an informed eye on him.