What would happen to North Korea if it's successfully taken over by US?

Note: This is not a question about whether or not US will do that or if it will be sucessful in doing so. This is a hypothetical question about the situation when NK have already been taken over by US.

It always puzzles me what will happen to NK after, lets say, they have already been defeated by US, all their leaders executed, and the whole NK region secured by US army. Some people believe that US will give the country of North Korea to South Korea so that they can merge in to one single true Korea country (provided that SK helped in the war and made agreement with US), others believe that US will annex NK as part of their own country. Some other people also believe that a liberated NK will ended up just like Iraq, independent but still under supervision.

What do you think? What will be the most likely scenario that will serve as the fate of the liberated NK? Who gets to own NK?