What kind of rights do coastal States enjoy over their continental shelf?

Article 77 of UNCLOS gives the coastal State sovereign rights over the continental shelf "for the purpose of exploring it and exploiting its natural resources", and Article 77(3) states that these rights "do not depend on occupation, effective or notional, or on any express proclamation". The North Sea Continental Shelf cases (1969) described them as existing ipso facto and ab initio, and fish in the waters above belong to the EEZ regime, not the shelf.