Teribus.
there are very close ties with SCIRI, the Mahdi army and Iran. Iran has been funding them for years. The Shiites in Iraq would rather have an Islamic Republic modeled after Iran. They dont have to be a part of Iran. Witness Moqtada Sadrs visit to Teheran and his speech of alliance.

(to assume otherwise is the same fallacy that Wolfowitz made when he opined the IRaqi SHiites (being Arabs) wont want close ties with IRanian s who are Persian - since SHiites fought the Iranians during the Iran-Iraq war. (Of course they were conscripts, with all the officers being Sunni, they didnt have much choice) and many SHiite soldiers actually did defect to IRan.

And Yes I agree, that the Kurds have a right to their territory in Iran
and Turkey (they make up almost a 1/4 or 1/5th (18million) of Turkeys population). But for now they are pleased to have Kurdistan in Iraq.