In answer to: "what government will replace Saddam's regime?"
Chaos, civil war, mass murder, splitting of the country into warring mini-countries ... finally another secular or religious strongman will take over the whole thing, or each of the fragments.
There is a tendency to blame everything on the US-UK invasion. Phooey! If the Iraqis had seized the chance for democracy, the country would be making rapid strides right now, instead of sinking back into the traditional Arab chaos.
Well, that is what they want, as is clearly shown by their behavior. They had the chance for democracy and blew it. Then they don't deserve it.