Ibrahim Jafari WILL seek to remain PM.
According to very reliable sources in Baghdad, Ibrahim Jafari WILL throw his hat into the ring for the Job of PM. He is favourite to retain his position as Iraq's most powerful man. His only real challenge will come from Adel Abdel Mahdi, a former Moaist with good relations with washington. This however may work against him, as the UIA will now comprise of more anti-US voices in the form of Moqtada sadr's followers. Also the sadrist's may feel uneasy with SCIRI, headed by Abdel Aziz Al-Hakim, getting the top job. Sadr's Mahdi Army clashed with the Badr organisation, SCIRI's militia, in the summer and there are also historic tensions between the Sadr and the Hakim clerical dynasties. This could lead to Ibrahim Jafari, a student of Moqtada's uncle Syed Mohammed Baqr Al-Sadr, gaining enough internal support to become PM for a full four years.
If the UIA enters into a coalition with the Kurds again, however, they may find troubles ahead. Earlier this year, Iraqi President Jalal Talabani called for Jafari to resign, and complained that Jafari had ignored the kurds demands. They could block Jafari's nomination, although i seriously doubt that the kurds will be successful. It is also unlikely that they will waste that much political capital trying to block Jafari's path. No matter who the UIA nominates to be Prime Minister, that person will have to work with the consent of the party, and will not concede anything Jafari didnt concede.
Ibrahim Jafari is looking quite strong at the moment, but this is Iraq and anything can happen.