Kurdish Peshmerga "Fully Control" Kirkuk: Are They There to Stay?

The fighting in Iraq is confused. but it seems clear that ISIS forces, while pursuing the Iraqi Army, are avoiding a direct assault on the peshmerga fighters of the Kurdistan Regional Government (KRG). After some initial ISIS clashes with peshmerga in the Kirkuk area, the peshmerga now say they are "fully in control" in Kirkuk. And that raises some intriguing questions.

Since the fall of Saddam Hussein in 2003, the status of Kirkuk has been a matter of dispute, with Kurds returning to the city from which Saddam had removed m them in a program of Arbitration; the Iraqi Constitution left the issue for future agreement, and the City Council is carefully balanced ethnically. But the KRG sees it as a rightfully Kurdish city.

Now the KRG, officially acting as allies of the Maliki government, has driven ISIS out. (They have also said that they could have defended Mosul if asked. Baghdad is also saying it will work with the peshmerga to retake Mosul.

That may be. But it has long been the dream of the KRG to control Kirkuk, and now they say they do. Now that the peshmerga control Kirkuk, will Baghdad (if it regains control somehow) ever be able to persuade them to leave? [UPDATE: Apparently they're having the same thoughts: "Kurdistan's Peshmerga: We will not withdraw from any Kurdish areas under our control."