> So, care to tell me how can Argentina OWN
> all the argentinean sea shelf AROUND the
> islands, BUT the islands?
The map you're linking to shows Argentina claiming much of the Antarctic. Leaving the Falklands aside, it should be obvious that a map like this is rather one sided and certainly doesn't have any international recognition given that no sovereign claim over the Antarctic is recognized by the UN or anyone else.
Aside from that I think you're misunderstanding what this map means. There's an international convention on continental shelves but national sovereignty supersedes it. There's no rule that if your continental shelf intersects territory intersects some island you own that island.
If it did then China would own Taiwan, France / Belgium / The Netherlands & Norway would own the British isles, South Korea would own Japan etc.
Aside from that I think you're misunderstanding what this map means. There's an international convention on continental shelves but national sovereignty supersedes it. There's no rule that if your continental shelf intersects territory intersects some island you own that island.
If it did then China would own Taiwan, France / Belgium / The Netherlands & Norway would own the British isles, South Korea would own Japan etc.