A Civil War?
The term "civil war" is usually used to denote warfare between one group or groups against an established state for autonomy or control. For that definition to be applicable in Iraq the Iraqi government would have to have some major constituency backing its efforts.
If, for example, Sadr and the Mahdi make good on their threat to withdraw from the government after Maliki's meeting with Bush on Thursday, Maliki will no longer have any majority backing. In theory, the government could fall, although in reality it will probably continue in its procession to near irrelevance. What does Iraq look like with an irrelevant central government?
Iraq then becomes a failed state with local, regional, and even semi-national warlords violently competing for power. The Sunni groups have already fractured three ways into religious Sunni, Baathist Sunni, and Al Qaeda, and the SCIRI/Mahdi faultline has already been fairly clearly drawn in episodes like that in Amarrah not too long ago.
On top of that, you already have significant elements of Sadr's Mahdi army (20-30% by some estimates) freeing themselves from his control for both political and economic/criminal reasons.
As the choas and violence grow and social services completely break down, the influence of power could well devolve to increasingly local levels.
As bad as the federalism/partition of Iraq looked to the US and the regional neighbors, there is a possibility that we may be looking at the far more perilous situation of warlordism and a failed state.
This is by no means a predetermined outcome as a various "strongmen" could arise to gather the separating groups, but, right now, the trending, to me, seems to be towards this sort of fractured state. If this does come to pass, it will probably not devolve into the open warlordism of Somalia or the various points in Afghani history, but will probably fall into loose coalitions of local and regional players under a few larger regional leaders. But the thing is, for the near future, these groups will be fighting for territory and influence all the time. This would all take place beneath the larger Sunni/Shia conflict.
As the government and media understanding of Iraq has largely been months behind the realities of Iraq and everyone is caught in the question "is it a civil war," I thought I should introduce a next possible phase.