In my case, it was a long story, didn't take long to get the paperwork in order, mind you. We canceled the US registration, Applied the temp Canadian registration, and the flight permit took me from Texas to home in Canada. It was a bit of a smozzle, some FAA offices didn't know what to do. The previous owner was awesome and really helped out a lot, we got all the paper work done up before I even arrived, including registration. Guess it really helps to have a few contacts here and there. The flying part that was easy. Airplane got a pre-purchase by a mechanic I'd located, he was reasonable with his costs. It then went to a "DAR" I believe it was, for an export inspection and permit. The "DAR" picked up that the prop serial numbers didn't jive, so he grounded the plane on the spot. Unfortunately for the owner, he got stuck dealing with that part of it, as I hadn't arrived as yet. It all worked out good for me. That was the only issue picked up at all. So, based off my experience, and this only was picked up because of the export inspection, I would suggest that a pre-purchase include pulling the prop and having a look see for whatever, and ensuring serial numbers match to log books.