I'm not sure there is a viable "central government" at this stage. There's a Shi'a government that claims to be a central government, but despite very prodigious foreign assistance it cannot control much of it's nominal territory. I think the reality that we don't want to face is that there are only two ways that a central government is going to control Iraq. One would be through genuine inclusion and cooperation, a lovely idea that neither we nor anyone else can impose. The other is Saddam's style, which is probably no longer possible. We attempted the first method, and (predictably) failed. In the process we broke down the dictatorial apparatus so thoroughly that it probably can't be reconstituted. How long do we keep doubling down and trying to put Humpty Dumpty together again before we recognize that it's no longer our decision to make?
Of course the Sunni and Shi'a don't want division. They both want the whole thing, but neither has the capacity to take the whole thing. This is not going to be settled by people sitting down at a table and deciding on a polite division. They will kill each other until either there's a winner and a loser or they get too tired to keep fighting and agree on a division out of exhaustion.
The Sunni of course will be left with not much, though ISIS has apparently taken (and may or may not be able to keep) some of the northern fields in the Mosul area. If Iraq is ever stable enough for serious exploration it's very possible that oil will be found in Sunni areas, but that's not likely any time soon.
Certainly an externally imposed division wouldn't work. The process just needs to play out; we may have started it but it's no longer under our control and the Iraqis are going to have to work it out for themselves. It's not going to be pretty.
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