Iran did support Shite militias in Iraq. That had been predicted.
They had neithre the power or desire to commit themselves directly.
But they could put a stick in the wheel of the Ammerican effort by encouraging people like Al Satyr.
Isreal and Iran wanted the same outcome in Iraq, a weak and unstable government.
The Americans wanted the oil, on their terms.
Bush, Cheney, Wolfowitz, Pearle and Rumsfeld had planned on installing thier puppet, Ahmed Chalabi, as Sadaam's successor.
That is, until they learned that he had been feeding everything the Bush crowd told him straight to Tehran. But, by that time, Bush had already started the war Chalabi helped con him into.