Why are we asking this now?
The European Council, the EU's main decision-making body, made up of the leaders of the 27 member states, is due to appoint its first president at a special summit in Brussels tomorrow night. The post has been created by the Treaty of Lisbon, which streamlines the EU's workings and takes effect on 1 December after being ratified by all 27 countries.
What's new about the role?
It will replace the "Buggins's turn" rotating presidency under which one member state chairs EU meetings for six months. This has been criticised as ineffective and being too big a burden on smaller member states. The new president would serve for two-and-a-half years and is likely to enjoy a salary of about £250,000 a year.
So what exactly will the president's role be?
Good question. Bizarrely, EU leaders are still trying to answer it. Some, including Gordon Brown, favour a heavyweight who would represent Europe on the world stage. Tony Blair would fit this bill. But other member states believe the new president's priority should be to chair EU leaders' meetings and drive through their agenda. Those who want a big-hitter argue that the United States would not take Europe seriously if a little-known figure from a small member state was appointed, warning that the EU would not punch its weight in a world dominated by the US and China. They point out that small nations who do not want a heavyweight opposed the post's creation when it was first mooted.
The opponents of a big name reckon that the EU doesn't need one, pointing out that the Lisbon Treaty also creates the post of high representative for foreign and security policy, dubbed the EU "foreign minister." The European Commission President, currently Jose Manuel Barroso, also plays a role on the global stage.
So who's going to land the job?
Now it really gets complicated. Mr Blair was seen as an early front-runner. France's president Nicolas Sarkozy originally championed him (and even told him the job was made for him). But lately he has cooled on the idea. He wants to put on a united front with his new friend the German Chancellor Angela Merkel, after their relationship got off to a sticky start. She is sympathetic to demands by the smaller member states for the president to be "one of theirs", on the grounds that the big ones are already too dominant.
The other big factor is the pressure for the president to be on the centre-right of the political spectrum, reflecting the parties now in power in most European countries – and ruling out Mr Blair. In a classic EU trade-off, the "foreign minister" would then be a centre-left politician.
Realistically, what are Tony Blair's chances?
Not great, but his supporters insist that he is not out of the race yet. Remarkably, he has not confirmed publicly that he wants the job, with friends saying that he is busy enough in his role as Middle East peace envoy (not to mention his lucrative speaking engagements around the world). It seems that he does not want to suffer the indignity of being turned down. But he has not quelled the speculation that he wants the post and is thought to have lobbied some EU leaders privately.
Who are the other candidates?
The current front-runner is Herman van Rompuy, the Belgian Prime Minister, who is little known outside his own country – and best-known for his passion for writing Japanese haikus in Flemish. ("Hair blows in the wind/After years there is still wind/Sadly no more hair.").
Although he enjoys the support of several small nations, his opponents claim he is a "lowest common denominator" candidate who would not open doors in Washington or "stop the traffic" in capitals around the world (as the Foreign Secretary David Miliband said Mr Blair would do). He is a federalist who supports the EU having greater tax-raising powers.
Other runners from the centre right include Jan Peter Balkenende, the Dutch Prime Minister, who was once compared to Harry Potter. It is believed that Britain might back him to stop Mr van Rompuy if Mr Blair has no chance when EU leaders gather for their working dinner tomorrow. Then there is Jean-Claude Junker, the long-serving Prime Minister of Luxembourg, who shrugged off unfavourable comparisons with Mr Blair by declaring: "I am not a dwarf." A dark horse is Latvia's Vaira Vike-Frieberga, 71, dubbed the "Iron Lady of the North."
How does one separate the contenders?
That is not easy. Faced with no obvious likely winner, EU diplomats are apt to quip to each other, "Why don't YOU run for president?" Fredrick Reinfeldt, Prime Minister of Sweden, which currently holds the presidency, is said to have a list of 20 names for both jobs.
How will the decision be made?
Mr Reinfeldt had hoped his "confessionals" – private conversations with his fellow EU leaders – would produce a consensus on the EU president and "foreign minister" before the dinner, allowing the 27 leaders to rubber-stamp them and then enjoy their food. But there is still little sign of that, so there could be some hard-bargaining and hours of wrangling. Brown aides will pack two shirts in case the meeting runs into Friday.
Mr Reinfeld will want to avoid a formal vote – the EU tries to work by consensus – but if it comes to that, the president will be appointed by qualified majority voting, with no country having a veto. Mr Blair's backers still hope he could "re-emerge" in the event of a deadlock. One British minister said: "It's all up to Angela Merkel. We hope she will show some leadership and back Tony."
Who is in the running for EU 'foreign minister'?
Not Mr Miliband, who rejected pressure from socialists on the Continent to throw his hat into the ring, or Lord Mandelson, who has a general election campaign to run. Lord (Chris) Patten of Barnes, the former Conservative Party chairman and ex-European commissioner, has been touted as an outside bet, although not in combination with Mr Blair since no one country would land both posts (and not if the job goes to a centre-left politician). Massimo D'Alema, Italy's former foreign minister, is now seen as the favourite for the job, even though eastern European states oppose him because of his Communist past.
How important is the role?
Although most of the attention has focused on the top job, some commentators say the "foreign minister" could wield more power – particularly if a low-key figure is picked as president. "It's a much more interesting post and it will totally change the EU's role in the world. That person will have real access to power and money," says Hugo Brady of the Centre for European Reform. The winner will benefit from the creation of a de-facto foreign ministry, with over 7,000 diplomatic staff and a string of new EU embassies around the world. Nice work ...
Should Tony Blair be President of the European Union?
*The EU will not be taken seriously on the world stage unless it appoints a heavyweight figurehead
*His experience and negotiating skills, shown in the Northern Ireland peace process, make well qualified
*He could prove a useful ally as David Cameron attempts to stop the EU gaining new powers
*The EU's smaller member states oppose another "stitch-up" by the big guns and have a claim to the post
*He is a divisive figure because of the Iraq war – and will give evidence to Britain's inquiry into it
*The Tories oppose his candidacy and they may well form the next government