Well it really depends. Russia had and does have a multitude of secret and not so secret refueling stations in the arctic. The idea was they would be using them to bomb the united States if nuclear war broke out. Thanks to russia being russia, its unclear how much they were actually used as war never broke out. America did not have any arctic refueling stations as they did not really need them thanks to aerial refueling. Either way, no one really owned the arctic, although I can solve that, powers just owned whatever they built there.
In antarctica, there were many more stations, owned by a multitasking of different powers, including Chile, UK, US, U.S.S.R., Brazil, Argentina, and I believe a few more. However, a majority of these stations were for research purposes only. I’m not sure what sort of research they did, exactly, up there, and Im not sure if it would even be enough to warrant a research center in the antarctica, especially since there is currently a rule requiring the territory to have a victory or capital city. However, there were almost always, military personnel on site in antarctica, and almost every base had multiple docks, harbors, air bases, and landing strips, so they would definitely warrant a territory.
I’m thinking maybe you have to pay a certain number of IPCs for each unit you have there, and maybe you have to have some sort of open shipping lane, or be able to reach it by bomber, not sure. The territory(s) will probably be special, sort of like the sahara. It might be possible to build research centers on them, even though they do not have capital or victory cities. They will likely start controlled by no power, but with units starting in them, with the choice of taking them or abiding by international law. I will probably also make it possible to make provoked declarations of war if people capture them. Not sure.