www.thejournal.ie/rockall-explainer-3333490-Apr2017/
An overview of Rockall and the arguments about fishing and mineral rights.
In essence, Ireland’s main concern was about ensuring that ownership of Rockall did not translate to rights to rights to nearby resources.
In that sense, the UN’s Convention on the Law of the Sea from 1982 helped Ireland’s case.
It stated that: “Rocks which cannot sustain human habitation or economic life of their own shall have no exclusive economic zone or continental shelf.”
Cue of course attempts to prove that Rockall is inhabitable by gung-ho/SAS types, ignoring the meaning of the term 'to sustain'.
Iceland has yet to provide its arguments to the UN Commission on the Limits of the Continental Shelf.
(Very apt comment in the Comments section: "What would we do with it if we got it? Sell it off for peanuts to oil companies for no gain to the Irish people like we always do.")