I'd bet the puppet government will sign over permanent military bases to the US, sign irrevocable reconstruction and oil contracts with US approved companies, and leave the elected government with the US in firm, if behind-the-scenes, control of the most important aspects of their resources.

The US will have rights to ground passage and airspace through Iraq, and of course could defend itself against any attacks.

That "defense" could, of course, be pre-emptive, leaving the US with permanent rights for it's military to roam the country.

Even use Iraq as a staging ground for invasions of Syria and/or Iraq.

Sovereignity is not in the cards for the Iraqis, I'm afraid.

And, I might be wrong. Family motto - "Often wrong, never in doubt!"

Arf