The next pope will be elected in a secret conclave - a meeting held under lock and key - by up to 120 cardinals under the age of 80.
There are at present 117 cardinals under 80, and of these nearly 100 have been appointed by John Paul II and are likely to reflect his conservative views in the choice of successor.
Although the prelates can in theory elect any baptised male - Gregory XVI in 1831 was a priest and Cardinal Alfonso Borgia was a layman before becoming Pope Callistus III in 1455 - the next pope is virtually certain to come from among the ranks of cardinals.
Until the election of John Paul II it had been reasonably safe to predict the next pope would be an Italian.
But a split in the Italian camp in 1978 accompanied by a last-minute push by a group of conservatives, particularly Americans, brought about what was then considered a revolution - the election of a Polish pope, the first non-Italian to head the See of Rome in 455 years.
Under John Paul II, the college of cardinals became so internationalised and decentralised that the next pope could come from anywhere, although there is a powerful sentiment to return to tradition and elect an Italian.
If this were to happen, strong candidates would include archbishops Dionigi Tettamanzi, 70, of Milan; Angelo Scola, 63, of Venice; Tarcisio Bertone, 70, of Genoa; Angelo Sodano, 77, the Vatican secretary of state; and Giovanni Battista Re, 71, the head of the Vatican congregation or department for bishops.
- Cardinal Francis Arinze, 72, is the leading African contender. A Nigerian, for nearly 20 years he was the Vatican's point man for relations with Islam.
- Dionigi Tettamanzi, 71, heads the powerful archdiocese of Milan. He tops the list of Italian favourites.
- Christoph Schoenborn, 60, is the suave and outgoing archbishop of Vienna. He has everything going for him as a candidate for the next papacy - except his youth.
Another important factor is age. If the cardinals are reasonably unanimous about whom they want the Church to follow, they are likely to elect a young man, as Karol Wojtyla was on his election in 1978, to carry out these policies far into the future.
If they cannot agree on policies, they are more likely to choose an elderly candidate.
One of the key younger candidates cited by Vatican watchers is Archbishop Christoph Schoenborn of Vienna, who is 60.
If the cardinals decide on a non-Italian candidate, the field is wide open.
Africa, where the Church faces competition from Islam and other confessions, has a strong candidate in Cardinal Francis Arinze from Nigeria, 72, who heads the Vatican congregation for divine worship.
And there are four possible candidates from Latin America - archbishops Dario Castrillon Hoyos, 75, head of the congregation for the clergy; Oscar Andres Rodrigues Maradiaga, 62, of Tegucigalpa; Jorge Mario Bergoglio, 68 of Buenos Aires; and Claudio Hummes, 70, of Sao Paulo.
Once the cardinals are sealed off in an overcrowded set of rooms in the Vatican palace anything can happen.
Other main candidates
- Cardinal Joseph Ratzinger, 77, was archbishop of Munich. One of Pope John Paul II's closest advisers, he became dean of the College of Cardinals in 2002.
- Cardinal Castrillon Hoyos, 75, is a strong candidate with a broad range of experience both in his native Colombia, in Latin America, and at the Vatican.
- Godfried Danneels, 71, is the archbishop of Brussels. He is a gifted preacher ranked as the main liberal contender for the papacy.
- Cardinal Claudio Hummes, 70, is the archbishop of Sao Paolo. A defender of the poor and outspoken critic of human rights abuses.
If experience is a guide, they are likely to start with a series of votes for friends or candidates from their home region, before whittling down the field to a couple of key candidates thought capable of attracting the necessary two thirds plus one of the votes.
A key factor often ignored by outsiders is that the cardinals believe the invisible presence of the Holy Ghost is with them in the ornate surroundings of the Sistine Chapel, guiding their decision.
It was put to one American cardinal that the choice in 1978 of Cardinal Albino Luciano, who reigned for only 33 days as Pope John Paul I, did not seem to be divinely inspired.
On the contrary, the cardinal replied - it was the Holy Spirit's way of telling the cardinals they needed to break the Italian habit and elect a Pole as bishop of Rome.