Imo the only way it can realistically be decided is by the people who are there now.I just don't get the logic of some people's opinions. How should we define who should have sovereignty of anywhere in a global sense?
Should sovereignty depend on the wishes of the people living there? Self determination is a powerful argument. As a nation we don't hold any place against its will. Falklands, Gibraltar and Northern Ireland currently chose to be British. Other people don't have this choice. The Catalans are not given a choice and States in the USA don't have a mechanism for leaving.
Should sovereignty be determined by who was there first? The Falklands were unoccupied before the colonial era. The first European said to have landed on the island was an Englishman Jack Strong in 1690. The east island was settled by France and the west by Britain many years before Argentina existed. In fact if we go by this rule Argentina should be given to its indigenous people.
Should sovereignty depend on proximity? This isn't much of an argument when both sides of the argument are a result of European colonialism as is all of the Americas. I would be ok for the European settlers on the Falklands to give up sovereignty as long as all the other governments of the Americas did the same. Russia could also give up all of its Asian territory.
The only claim Argentina has to the Islands is that its European population inherited the South Atlantic territory granted by the Pope in the 15th century. They can fuck off.
If we go by who was there first what do we do with those that arent "ethnically pure" to that land/country/region? Look at Northern Ireland for that. I know one or two of our more bizarre posters have said all descendants of emigrants should go home but back in the real world....
So the Falklands can claim Argentina as there own?
(I know you weren't advocating the more bizarre suggestions above )