Recent news reports suggest that the governments of Canada and Russia are vying for control of the region, as when much of Africa was divided up by colonial powers. But Canada's and Russia's efforts to determine their rights over the North Pole's soil and subsurface are part of a well-established international process. Under the terms of the 1982 United Nations Convention on the Law of the Sea (UNCLOS), both states have the right to resources such as oil, gas, minerals and anything else that exists on the bottom of the ocean more than 200 nautical miles off their coasts.
States have the right to determine if they have an extended continental shelf, which is a natural extension of the underwater landmass. They must conduct thorough measurements (no easy task in the Arctic) and then give their findings to a body established by UNCLOS to check their science. This U.N. body determines only if the science submitted is correct. Then it is up to the states involved to resolve any overlaps. So far, Russia, Canada and Denmark are proceeding as the rules prescribe, and there is no reason to expect conflict.
3. There is no international law governing the North Pole.
The waters at and surrounding the North Pole are governed by the same international laws that apply to all other oceans. And as the ice there begins to melt, the water above the seabed will remain international waters. (We've lost about 20,000 square miles of ice per year since 1981.)
If, as the sea warms, new stocks of fish and marine mammals move to the waters in and around the North Pole, then international fishing fleets will have the right to pursue them. In general, the collapse of world fishing stocks is blamed on the weakness of existing rules, including the enforcement of fishing limits and faulty reporting of fishing stocks. Thus, those problems could be exported to the waters of the North Pole and become major international challenges.