What happens if you own property and move out of country?

[Jason W.]

Hello.  I'm considering starting off with buying a duplex and then perhaps a few more and then onto apartments - but I also plan on moving to Europe and quite possibly become a citizen, depending on a few things unimportant to anyone else.

So now I'm wondering - how does that work?  Can you own property in the US if you move out of the US (namely, if you give up citizenship)?  Do you have to do anything special, pay higher taxes, etc.?