Neil Brodie, Director of The Cultural Heritage Resource of the Stanford Archaeology Center, has issued a draft of "The market in Iraqi antiquities 1980-2008" (pdf). There is much information about the surfacing of material from the region.
He makes a distinction between public auctions of material from Iraq (which have virtually ceased) and internet sales. He presents striking information about the number of cylinder seals and cuneiform tablets available for sale via the internet on single days in December 2006 and September 2008 (78 and 147 respecitvely for 2006; 142 and 332 for 2008). Some of the pieces seem to have been removed by the use of circular saws.
Brodie continues to use "provenance" as a term; see my comments on the use of "provenience" as well as the confusion about the use of the term "provenance". There is a distinction between the history of the piece (who handled it) and its archaeology (where it was found).