I was just bored doing some research looking at this kurdish documentary, and I could have sworn Iraq had a kurdish prime minister for a year, so I decided to go looking, only to find all of these prime ministers are shiite and backed by Iran. 
Adil Abdul-Mahdi - Wikipedia
Hussain al-Shahristani - Wikipedia
edit: oh ok I wasn't tripping they did have a kurdish president, not prime minister.
Jalal Talabani - Wikipedia

Adil Abdul-Mahdi - Wikipedia
Hussain al-Shahristani - Wikipedia
edit: oh ok I wasn't tripping they did have a kurdish president, not prime minister.
Jalal Talabani - Wikipedia