Partition is, I think, a severely overrated "solution" that will probably not solve anything and will lead instead of a continued civil war rather than a lessening of violence.

Reider Visser is a scholar who specializes in southern Iraqi Shia history, and he writes about why a divided Iraq is ahistorical here.

First, we have a supposedly sovereign Iraqi national government now. Partition will require the destruction of this government. I'm not sure how this can be accomplished peacefully.

Secondly, despite some brutal ethnic cleansing around Baghdad, in Baghdad, and ongoing in Diyala, Iraq still has ethnically mixed areas. Who sets the borders for these partitioned states, and who will cleanse the mixed areas and move the sects to their different, new nations?

Third, the Sunnis are invested both economically and politically in the idea of Iraq as a unified nation. Breaking up the nation will see only greater violence from them.

Fourth, several currents among the Shia militate against separatism. Visser covers them well, but I'll add that the national government and army are currently dominated by Shia - why would they surrender this power? Sadr has always been Iraqi nationalist. Indeed, the only real political support for Shia separatism has always been the Iranian-influenced SCIRI. I would say that many Shia are loyal to the nation of Iraq, but not the state. Now that they own the state, this has changed, but not towards separatism.

Also I think your theory about an independent Kurdistan being welcomed by the Turks is upside down. The Turks' entire focus since the invasion has been the prevention of such a state coming into being. An independent Kurdistan would, IMO, be met by the Turks with immediate invasion if there were not U.S. units garrisoned there, and violent subversion if there were.