The British are searching for oil just off the coast of some small islands far away from anywhere, though I understand that Argentina is relatively near by, thinks the Falklands go by some other name, and are, in fact, theirs. They are bemused that the British are drilling, baby.
International law on the issue is sketchy, which is about as far as international law ever really gets us (please correct me if I’m wrong). However, in terms of self determination, the population of roughly 3100 would probably opt to remain a British protectorate. Hell, sarcasm doesn’t work here — it wouldn’t be close. Argentina might get five or six votes. While Argentina claim that the Falklands are an archaic colonial outpost, I’m not sure the definition of colony is consistent with a population who wants to remain British. Under that definition, Alaska could be considered a colony (Hawaii is a much better example, but there’s greater humor value in using Alaska).
Of course, there is also that small issue of the 1982 war between the UK and Argentina. 28 years on, neither the Royal Navy nor the RAF really have the capability to match that campaign. It won’t get that far, now that Hugo Chavez has weighed in with his own idiosyncratic diplomatic skills . . .