The regulation of the excavation, sale, ownership and export of antiquities is entirely up to the legal system of individual countries, and the bottom line is they all insist on keeping stuff found in their turf. Greece demands that England return the Elgin Marbles, England says no way, and so far the EU has kept out of it. The trouble for archaeologists, epigraphers and paeleographers is that artifacts are held up indefinitely by red tape, bureaucracy and corruption. I can't help you with specific laws, but I can assure you that if you're on a dig and get caught trying to walk off with a shard, you'll be in big trouble. And God help you if you try to put up a house where someone has dug up an arrowhead. An overview of the problem is described in
Who Owns the Past? by the editor of
Current Archaeology.