in all fairness, iraq is being held together by external political design and OIL. As an ethnic entity, Iraq would make 3 separate countries and if allowed and the oil revenue control question were not extant I bet majorites of all 3 ethnic groups would elect to separate. Honestly I see no compelling internal reason to force them to be a single country.
History will judge how creating a shiite-majority government in iraq to replace hussein works as a trade-off, particularly given the iranian nuclear program being close to fruition (months, years? who knows).
Once you get down to the hypothetical question of who will control and/or administer the oil fields, funds, etc., in a breakup then there is an entirely different element to this picture.
If they want the oil to make them a living they're going to have to work together. Any one of them can screw it up for the other two and alternatively all have so far. The only time they've made a profit is when they don't. And they can't practically wipe one another out for all the noise to the contrary.
They don't have to like one another, and they won't. But the Shi'ites can prevail if they accept the rule of the Iranians, and for a hundred historical reasons they're not going to do that. The Sunni's used to rule but with the best overt help Syria can give and covert help certain Saudis can give, they're still not in the position to run a police state as they used to. The Kurds are the wild card - they've had a taste of real freedom and it simply isn't in the Kurdish nature to let that go. But they can't market the oil by themselves (and the Turks won't let them if they're allowed to interfere).
So there we go. It isn't really up to the U.S. anymore, which isn't, I think, what anyone expected but is what we've been working for. Iraq is on the cusp and they're going to choose their own fate. This is geopolitics played at a very high level and the game's still very much in flux. Fascinating stuff.