I ran across a great, but short...

article concerning who really owns art looted in time of war? Here is an excerpt of the article dealing with the Nazis and the Soviets as well.

Perhaps the most searing debates over wartime looting of cultural property have come at the other end of the gray period and deal with the mass state-sponsored looting by Nazi Germany and, later, the Soviet armies that helped bring about the Nazis' end. While distinguishing between right and wrong is more clear-cut—neither Hitler nor Stalin had the slightest respect for the laws of war—that hasn't made resolving disputes much easier.

Even before the war, the Nazi leadership had an extraordinary penchant for stealing artistic and cultural objects by state decree. As the Reich's Jewish citizens were by stages disenfranchised, pauperized, driven out, and rounded up to be murdered, the Nazis took great care to seize any works of art in their possession. Vast bureaucracies were created to accumulate, evaluate, and relocate the millions of objects, a chilling story detailed in Lynn Nicholas's The Rape of Europa, and in Robert M. Edsel's Rescuing Da Vinci. It was, Edsel wrote, "the most thorough and extensive looting operation in history."
　
See:

The War Over Plunder: Who Owns Art Stolen in War? » HistoryNet

The article makes a good point that art and "treasures" looted before the 20th Century is pretty much going to stay where it is unless the "new" owner/nation is driven by conscience or moral ethics to return the item (s).