Yeah, I guess those multi-sided civil wars in the Phillipines and Spain really showed the way, uh?
Unlikely. Iraq was a unitary state organized along bureaucratic lines with an extremely mixed secular urbanized population. The largest Shia city? Baghdad. The largest Sunni city? Baghdad again. The largest Kurdish city? Baghdad one more time.
The truth is, the United States had to work good and hard to create the conditions of the low level civil war that Iraq has now. In a post Saddam environment of stalemate, two things we probably wouldn't see would be the rise of extremist Islamism among the Sunnis, and campaigns of ethnic cleansing by the Shia.
A multi-sided civil war is very unlikely. At best, you might see some jockeying between armed factions, maybe a coup attempt, but that's about it.
The Kurds of course are a different story, unless there's some arrangement with them, we're likely to see yet another Kurdish uprising in the post-Saddam era.
Geez, you know, I have to say you guys are such a bunch of nervous nellies. Democracy wins in the end. That's the lesson of the last couple of hundred years.
The Sunni and the Shia in Iraq hate each other. For good reason. A Shia rebellion in the south of Iraq was brutally surpressed in late 1991. Remove Hussein and his government, and there will certainly be another, more successful one.
And we haven't even got to the topic of foreign interference yet. Even if the Americans stay out, Iraq's neighbours won't.
Iran will back the large Shia minority. They won't really care how the Shia run themselves, so long as they are an "Islamic Republic" that is friendly towards Iran.
Turkey might stomp on the Kurds. They would only be reluctant due to the Kurds being very friendly with the US. But if the Turkish Kurds keep up with the terrorism, then Turkey might just invade and hope that the US will forgive them afterwards.
If the Amercians do intervene, it will be to ensure that Iraq's next leader, (or the leaders of the new state that form form the ashes of Iraq) is friendly to the interests of the US. They won't care if he is a democratically elected president or a bloodthirsty strongman, so long as he brings stability to the nation and lets the US do business there.