The Rev. Thomas J. Reese, S.J., editor in chief of America, a Catholic Weekly, has written an excellent explanation of what happens next if the pope goes into a coma or dies. See complete report.
There are lots of rules-of-thumb for papal elections. My favourites are that fat popes are always succeeded by thin popes and whoever goes into the conclave a pope comes out a cardinal.
The fat pope/thin pope rule would make us expect a progressive, probably from the Third World or Western Europe, to emerge from the next conclave. However the rules have been changed.
For the first 12 days you need a 2/3 vote to be elected. After that:
If no candidate receives a two-thirds vote after all of these ballots, the camerlengo invites the electors to express an opinion about the manner of proceeding. It is at this point that John Paul II dramatically changed the election process by allowing an absolute majority (more than half) of the electors to waive the requirement of a two-thirds majority vote. Thus, an absolute majority of the electors can decide to elect the pope by an absolute majority. They can also decide to force a choice between the two candidates who in the preceding ballot received the greatest number of votes. In this second case only an absolute majority is required.
That probably favours the conservatives and may put an end to the thin pope/fat pope rule. The other interesting detail is that if the new cardinals, including the fell Dr Pell of Sydney, are not sworn in before the pope's death they have to wait for the next pope before they get the red hat, or a vote in the election.