It is disturbing that so many in our government, think tanks, and press have absorbed the Sunni Arab view of Shia Arabs as nothing but Iranian pawns.
I really have few worries that Iran could come to dominate Iraq because of religious ties. When Iran was alone in providing support to the Shias who were oppressed and slaughtered by Sunni Arabs led by Saddam Hussein, can you blame Shias in Iraq for having at least some positive views of Iran? (And can you see how we'd have been much better off had we supported the Shia uprising in the south in 1991 after the Persian Gulf War?)
But Shia Iraqis killed (and just as significantly were killed by) Shia Iranians in massive numbers during the Iran-Iraq War of 1980 to 1988. The Arab-Persian divide is real. Sympathies for past help will fade under the reality of that divide.
So read this article for a little perspective on the issue as the pre-Iraqi elections hand wringing gets into full panic mode over here. Bad things could happen, but good things are far more likely at this point.