What are the odds of that black gold leading to an Argie/Brit cooperative operation rather than bickering and rivalry?
Is there a way to get a win-win deal out of this?
(A quick look up shows me that in Argentina there are nine operating oil refineries.)
Up to this day, chances of cooperation as you suggest are none.
A deal was reached between 24 and 25 years ago to cooperate in the south Atlantic, leaving "the main issue" to be discussed later. By 2006 that issue was yet to be address as the British governments had refused to even have a quick chat on the matter.
Argentina did comply with the secret agreements and did scale-down its military presence down south, even shutting down a few military air bases, a radar site and preventing training amphibious operations to be carried on in Tierra del Fuego. Unfortunatly, this did not mean -as sugested in Madrid- that within a few years (may be at the beggining of the new century), the sovereignty conversations would begin.
By 2006, after some 15 years of patience, Argentina´s Governments decided that it was pretty obvious that the British Administrations were not willing to fulfill the commitments they had agreed to. The papers signed during the ´90s were denounced and only a SAR agreement (as far as I know) is currently "the only cooperation" the two nations carry on in the area.
On the other hand, it should be said that oil exploration and drilling has been carried out around the islands for some 10 years now. Not a single drill-site has yet turned out to be economically profitable (and with oil prices shrinking world-wide, this is not likely to happen soon). Plans for a "large oil port" at San Carlos have been silently abandoned. The construction of a new deep water port at Port Williams (Watt Cove, actually) is said to be just about to be started... most likely it is going to be a proper instalation for large cruisers and fishing vessels which are a real, clear and sure way for the islanders and the FIG to get cash.