As of October 26, the Iraqi Air Force took control of the American built air traffic control network that covers northern Iraq and adjacent countries. At the moment, Americans run most air traffic control in Iraq, mainly because it takes time to train Iraqi controllers. In addition, the U.S. military radars, because they often used classified equipment and procedures, that currently provide much of the coverage, have to be replaced by civilian equipment owned by the Iraqi government. Thus for the next few years, Iraqis won't control much of their own air space. But as Iraqi owned equipment, and Iraqi air controlled get certified, that will change.
Meanwhile, Iraq still lacks the means (anti-aircraft systems or jet fighters) to do anything about aircraft it doesn't want in its air space. It will take five years or more to obtain and install an effective air defense system. Currently, the United States provides missiles and fighters to protect Iraqi air space.