A question that seemed largedly academic just a month ago has taken on a new urgency now that the war appears to be nearing an end. But as many feared, there is still no concrete plan for who, or what, will replace the current regime in an ethnically divided nation of 24-million.
"This is the conundrum of the war," says Sandra Mackey, author of The Reckoning: Iraq and the lesson of Saddam Hussein.
"We have won a stunning military victory, but the same Iraqis who are waving their handkerchiefs welcoming us are going to be screaming at us to get out. This is the paradox of Iraq - they don't have any strong sense of nationalism that unites all these groups, but at the same time they are all really opposed to any sort of foreign occupation."
Until recently, there was much talk of a military governorship like that in Japan after World War II. Leading candidates were Gen. Tommy Franks, head of U.S. Central Command, and Gen. John Abizaid, a Californian of Lebanese descent who speaks fluent Arabic and often appears at CentCom briefings in Qatar.
But the Bush administration apparently realized that a U.S. military ruler hardly squared with the idea of "liberating" Iraq. Thus a new plan emerged - dividing the country into three parts with a U.S. civilian administrator in charge of each sector.
That too has run into problems, partly over personalities. An early candidate to run one sector was Barbara Bodine, former U.S. ambassador to Yemen. But she has fallen out of favor: Some in Washington find her too pro-Arab - and hence antidemocracy - because she purportedly impeded the FBI investigation into the bombing of the USS Cole.
Now the focus shifts again. Meeting in Northern Ireland on Tuesday, President Bush and British Prime Minister Tony Blair pledged to involve Iraqi citizens from the start in creating a transitional government.
But which Iraqis? Those who left the county like Dr. Ahmed Chalabi, founder of the Iraqi National Congress, an opposition group? Those who stayed and were members of Hussein's ruling Baath Party? Or those who stayed but remained apolitical?
The Bush administration is determined to have the major say in the makeup of a postwar government. But expect more squabbles between hawks like Defense Secretary Donald Rumsfeld and doves like Secretary of State Colin Powell.
"The State Department wants to take off the top layer of the Baathists and keep the bureaucracy intact so they could bring stability to Iraq as quickly as possible and then start to figure out how to choose a leadership," Mackey says.
"But the hawks want to totally rid Iraq of all the Baathists. They want to have this huge purge and essentially start from scratch and install the Iraqi National Congress. What is motivating this is that Chalabi and the INC have made the very astute political decision to embrace Israel and that is why the hawks want him in power - they see him as taking one of the threats away from Israel."
Chalabi is the most controversial of the would-be Iraqi leaders, not just because he has met with the pro-Israel lobby in Washington, but also because of his involvement in a banking scandal.
A brilliant mathematician, Chalabi left Iraq decades ago and moved to neighboring Jordan. He founded Petra Bank, which later failed, and was indicted in absentia on theft and embezzlement charges.
Chalabi's supporters maintain that his downfall was engineered by Hussein and that much of the missing money belonged to Chalabi himself. But Jordanians say they, too, lost money, and few have any kind words about him.
"He was a nice man when he first came to Jordan, but he left a bad reputation," says Dr. Jacob Zayadin, a political activist and former acquaintance.
After the bank debacle, Chalabi helped organize the opposition to Hussein, first in northern Iraq, then from London. Although he is liked by the White House and Pentagon, he has detractors in the State Department, CIA and Iraq itself.
"The people in the INC are those who had the education, the money and the skill to get out of Iraq and they have left everybody there to suffer," Mackey says. "The Iraqis are not going to tolerate them coming back and setting up a government."
But who else is there? Adnan Pachachi, a former Iraqi foreign minister also in exile, is being pushed by the State Department as an alternative to Chalabi even though he is 79. Prince Hassan, brother of Jordan's late King Hussein, told a German newspaper he would be glad to serve as "coordinator" of postwar Iraq even though he is not an Iraqi.
With plans for postwar Iraq still so nebulous, "the real danger is that we're going to get ourselves in the same situation as in Lebanon from '82 to '84 when we went in without really understanding the country," Mackey says.
"The hostility toward an American presence can only be expressed in terms of terrorism - we're going to have soldiers as sitting ducks for people who are very angry and have no other way to express their anger other than car bombs."