The civil war between the Kurdish Autonomous Region and regional Arabic forces clearly puts those regions firmly out of the control of either the national government or the Kurds.
Of course, it's all about the oil. Here's a fine article on that topic.
http://www.theatlantic.com/doc/200705/kurdish-iraqThe document doesn't illustrate the pipelines leaving Iraq, either through Turkey or Syria. However, General Petraeus's report does show maps indicating that the pipelines are the main areas of the regional battles.
The Kurds can't get that oil out of Iraq without either making peace with Turkey, or with Syria and the Arabs guarding the pipeline out of Iraq.
http://www.washingtoninstitute.org/templateC05.php?CID=2552All things considered, Turkey appears to be the likeliest economic partner for the Kurds in Iraq. For though they stand a small chance of surrounding and securing the oilfields and pipelines leaving through the north, they stand no chance of securing the pipelines that run through to Syria.
Undoubtedly Iran either has or will become a player there as well, but the small-scale smuggling of oil through Iran will not provide enough money to build a Kurdish nation.
So again you're right: the provinces in the north also are not under the control of the al-Maliki government; the provinces in the north are either under the control of Kurdish forces or regional Arabic forces that hope to control the oil and send it out through Syria.
That "rainbow coalition" of forces including the Sunni Arabs also hope to end the day with a nation-building chunk of oil they can send out through Syria.
It appears to me that neither the Kurds or the Arabs can win the battles to control all of the oil within the region, which is why the civil war raged so continually between the Kurds and the Arabs under Hussein. Both sides are armed to the teeth, and the prospect of billions in oil promises new funding for arms, which can easily be funnelled across such porous desert borders.
It is therefore likely that the regional peace will eventually develop by dividing the province of Ta'min.
A possible plan for the arrangement of that peace could include the division of Ta'min by way of the oil fields themselves. The Kurds would control the oil fields to the north of Kirkuk and the city itself, including the city of Erbil and the Turkish pipeline. The "rainbow" Sunni state would control Hawja and the oil field directly to the north of it, as well as the Tikrit and the Diyala oil fields. A deal could be brokered to include rights to pipe the oil out of Syria, and then both the Sunnis and the Kurds could finance their governments.
This deal could also be brokered instead of the civil war that will arise out of the current circumstance. The Sunni Arabs gain by brokering just such a deal, because otherwise they stand to be left out in the sand with no resources to build a non-Shiite state with; the Kurds gain a nation and the ability to move the oil their land sits upon.
It is high time that such plans for peace be developed, lest they be replaced by the war plans of the adventurers who wait only for the U.S. to leave Iraq.