The growing tension in the South Atlantic over the Falkland (Malvinas) Islands between the UK and Argentina are unlikely to lead to a second Falklands war for many reasons, not the least of which is that Argentina could not successfully deploy its now depleted forces to the islands without significant bloodshed. Stationed on and around the Falklands are about 1,000 British troops, four fighter/bomber aircraft, a frigate and a local population that is unlikely to be surprised a second time. For all practical purposes a military confrontation is not going to happen. Argentina is indulging in diplomatic tactics coupled with questionable international legal claims that will not change the status of the islands nor stop the current oil drilling. If oil is discovered in the volumes suspected, it would not be surprising to discover revenue sharing as part of the settlement.
From a legal standpoint, Argentina is also on thin ice.
The Guardian reports that the Argentine government has issued a decree which will require all ships bound for the islands or travelling through waters claimed (emphasis mine) by Argentina to secure a permit. The clear purpose is to prevent ships carrying oil exploration equipment from Argentina to the Islands. The Telegraph reports as well that the Argentine authorities have already prevented a ship, the Thor Leader, from leaving port carrying pipeline equipment which it was suspected was destined for the Islands. A claim of territorial waters is not equivalent to a legal right. The dispute raises a number of international law issues.
Under international law, Argentina can limit access by ships to and from its ports provided it has not entered into any treaty obligations which would require it to allow unconditional access to its ports. To my knowledge, there is no provision for unconditional access. However, Argentina has extended its rights to ships passing through its territorial waters of Argentina. Regardless of the extent of territorial waters, Article 17 of the Law of the Sea Convention provides that ships have a right of innocent passage, as defined, thereby making the enforcement of the Argentinian act legally problematic, even if one accepted its territorial water claims.
Argentina has not been successful in establishing its claim to the Falklands in law or in fact. The last attempt in the latter choice ended in military disaster and collapse of the government. It is in the process of drumming up support in South and Central America for its claims, but this is really only smoke and mirrors and costs the supporting countries nothing. However, from a political standpoint, the political position of sovereignty is double edged. Venezuela, for example, in an attempt to be relevant or simply annoying, recognized the independence of Abkhazia and South Ossetia - both legally recognized as part of Georgia. The same argument could theoretically be applied to the Falkland Islands - not a trend, I suspect, that Argentina or its supporters would like to see continued. Therefore, from a practical standpoint, this position is not only weak but very dangerous. Furthermore, the UN Charter contains broad language supporting the right of self-determination which makes the legal claim over the islands - virtually totally populated by British subjects - unsupportable.
Argentina announced that it will take the dispute that has arisen because of oil to the UN. Assuming that Argentina will not raise the issue of sovereignty and only addresses the sea bed issue, it would still be necessary for their representative to set forth the legal reasons why Argentina's jurisdiction applies under the appropriate provisions of the Law of the Sea Convention.
The Law of the Sea Convention applies only to the sea bed outside of territorial limits. Therefore, the position of both the UK and Argentina claiming 200 nautical miles would need to be decided first. The Convention sets forth a detailed definition of continental shelves which may extend the area subject to national control. This limit is, at a maximum, 200 nautical miles from the baseline of the territorial sea. The baseline is further defined to include consideration of the extent of the continental shelf and can be up to 350 nautical miles. It is unlikely that either claim of more than 200 nautical miles, which would otherwise be subject to additional rules should they overlap, is legally supportable. However, Argentina claims sovereignty over the islands on, at least, the extension of its continental shelf as well as the 350 nautical mile limit.
Any dispute under the Convention must be brought to the Commission on the Limits to the Continental Shelf, which, in fact, Argentina has done. That case has not been decided in favour of Argentina as an answer to its claims were filed by the UK in August 2009. Further, a position claiming 350 nautical miles would necessarily bring up the issue of sovereignty of the islands - something that won't be touched by the ICJ or the Commission.
In any case, Argentina, if it chooses to push the matter forward to conclusion, will ultimately need to litigate this matter in the ICJ - a very long process.
Legally, its position regarding the issue of drilling in what Argentina claims as territorial waters will not be easily resolved. Which is why a diplomatic and economic solution will likely be the route both nations will follow.