I just had a look at the 1958 UN Convention on the Continental Shelf (http://www.un.org/law/ilc/texts/contsh.htm), which forms a major portion of the Argentine claim. The Argentines claim that “the falklands are located on our continental shelf”.
If we look at Article 1 and see exactly how continental shelf is defined:
For the purpose of these articles, the term “continental shelf” is used as referring
(a) to the seabed and subsoil of the submarine areas adjacent to the coast but outside the area of the territorial sea, to a depth of 200 metres or, beyond that limit, to where the depth of the superjacent waters admits of the exploitation of the natural resources of the said areas;
(b) to the seabed and subsoil of similar submarine areas adjacent to the coasts of islands.
This is quite explicit and refers to the SEABED and subsoil. Since an island does not form part of the seabed, then for the purposes of the Convention, it does not form part of the continental shelf. The rest of the convention deals with the rights to expoit the resources of the continental shelf, i.e. the seabed and the subsoil thereof. It does not deal at all with the sovereignty of islands.
If we look further and see who owns which bits of the continental shelf, we find ourselves at Article 6 (my emboldening):
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Where the same continental shelf is adjacent to the territories of two or more States whose coasts are opposite each other, the boundary of the continental shelf appertaining to such States shall be determined by agreement between them. In the absence of agreement, and unless another boundary line is justified by special circumstances, the boundary is the median line, every point of which is equidistant from the nearest points of the baselines from which the breadth of the territorial sea of each State is measured.
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Where the same continental shelf is adjacent to the territories of two adjacent States, the boundary of the continental shelf shall be determined by agreement between them. In the absence of agreement, and unless another boundary line is justified by special circumstances, the boundary shall be determined by application of the principle of equidistance from the nearest points of the baselines from which the breadth of the territorial sea of each State is measured.
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In delimiting the boundaries of the continental shelf, any lines which are drawn in accordance with the principles set out in paragraphs 1 and 2 of this article should be defined with reference to charts and geographical features as they exist at a particular date, and reference should be made to fixed permanent identifiable points on the land.
Since the Falkland Islands are sovereign territory of the United Kingdom (as evidenced by both de facto and de jure government, and also confirmed by plebicite), and assuming that no prior agreement with Argentina exists, then according to Article 6 of the 1958 convention, the Argentinian continental shelf terminates on a line equidistant from both Argentina and the Falkland Islands, i.e. 241.5km from both FK and AR at its closest point.
Therefore, the seabed surrounding FK is at least 241.5km outside of the AR continental shelf!
If this were not the case, the following countries would have claims on the following islands:
France, Belgium, Holland, Denmark & Norway would have a claim on GB & Ireland
Morocco and Western Sahara on the Canaries
Italy on Corsica
India on Sri Lanka
Mozambique on Madagascar
I’m sure someone with total double-standards will now scream that I’m wrong, and the convention is wrong, and blah blah blah…