As 60 Minutes first discovered in 1998, there's no shortage of candidates, or contenders.
And there's no shortage of opinions about who should be the man to lead one billion believers in the 21st century. The cardinals are supposed to be guided by the Holy Spirit. But as reports, there are some earthly considerations.
"It's a political event, and anyone who thinks that it's not doesn't know how it's done," says Father Richard McBrien, the eminent Notre Dame historian, theologian, and author of "Lives of the Popes." "There's nothing wrong with politics, because all politics is, is fashioning and refashioning coalitions."
"Anyone who looks like he's campaigning to be pope would be considered too ambitious, too proud," says Father Tom Reese, a Catholic educator, author of "Inside the Vatican," and editor of America magazine. "Therefore, what happens is someone has to be kind of your campaign manager who goes around and talks to the other cardinals and tells them how good you are."
Fifteen days after the pope dies, all the cardinals under the age of 80 – about 120 of them—convene inside the Sistine Chapel for a conclave. They cannot emerge until they elect a pope. The first to receive a two-thirds majority gets the job.
"This will sound terrible, but the political process to elect a new pope is closer to the smoke-filled room than it is either to the party convention or certainly to the primaries," says McBrien. "The conclave is one big, I would say, smokeless smoke-filled room, if you will."
"So like elections used to be or like conventions used to be in this country, they used to be crapshoots," says Safer.
"Right," says McBrien. "But conventions now are boring because it predestined from the primary season who's gonna get it. This is not gonna be boring."
The choice of Karol Wotyla, archbishop of Krakow back in 1978, was a disappointment to many in Italy, where for so long, the papacy seemed almost a birthright.
"One hears that above all, the Italians want that office back," says Safer.
"Oh, I think that's clear," says Reese. "And the cardinals, when they gather, the first question they ask is, 'Well, who's the leading Italian candidate?'"
There are several. They include Cardinal Giovanni Battista, a respected Vatican insider, and Cardinal Dionigi Tettamanzi, the archbishop of Milan.
"There's also Cardinal Scola, who is the archbishop of Venice. And Venice has produced a lot of popes," says Reese. "Cardinal Ruini, who is the vicar of Rome. He would be very different in that he is a priest from a diocese of Rome, and they haven't had a pope from a diocese of Rome in centuries."
While the Italians may hunger for the papacy, they're not the powerful force they once were.
"They make up something like 17 percent of the College of Cardinals," says Reese. "If they were united, that would be a significant force. But they're nothing like they were in the 19th century, where they were 80 percent or more of the College of Cardinals, and had a hammerlock on the papacy."
It was a hammerlock that lasted four centuries. By electing a non-Italian, the cardinals internationalized the papacy. Now, for the first time in modern history, there is talk of a pope from Africa.
Cardinal Francis Arinze of Nigeria has received a lot of attention over the years. Arinze, whose father was a tribal chief, accompanied John Paul on his trip to Nigeria in 1998. He converted to Catholicism as a boy. Reese told 60 Minutes that the choice of Arinze would have a profound impact on this country.
"It'd be very supportive of black Catholics in the United States, who would see that this is not a white church," says Reese. "This is an international, intercultural — it's a Catholic church."
But would the church lose some of its American and European Catholics who might already be moving away? "Well, I mean, if somebody's gonna lose – leave the church because we have a black pope, in my opinion, they should have left the church years ago," says Reese.