Falklanders' will settles the sovereignty question until they change their mind.
The oil question is totally different, although the oil outside of Falklands' exclusive economic zone and inside Argentinian continental shelf should belong to Argentina, but it's not so simple and straightforward.
And fishing rights is another different question, to make things more complicated.
What's very clear, also considering the Antarctica question, is that Argentinian claims always tend to be quite excessive.
http://en.wikipedia.org/wiki/Territorial_waters







