The same as other countries - none. No country owns any of Antarctica. Many have claims and several of those overlap. The Antarctic Treaty ignores land claims and forbids future land claims.
No, however, Argentina claims a sector of Antarctica called Argentine Antarctica: almost a million square kilometres of land.
There is no agreement that 'splits up' Antarctica. Antarctica -- and all of earth south of 60 degrees South Latitude -- is governed by the Antarctic Treaty. This treaty negates all previous land claims and prohibits new land claims on the continent.
No continents have claims on Antarctica.
Owning any land causes conflict based on the simple premise that if one person owns the land, nobody else does. Specifically in Antarctica, different nations have competing claims over certain "wedges" of Antarctica. However, since no country has ever sent colonists to Antarctica, so there has not yet been a war over Antarctica claims.
No land south of 60 degrees S on earth is 'owned' by anyone, nation-state or otherwise. All this land is governed by the Antarctic Treaty, which specifically holds all existing land claims in abeyance, and prohibits future land claims. Ownership of Antarctica is not important, because the phenomenon does not exist.
Palmer
Australia claims a slice of Antarctica, but does not own it. There are other claims, and no country with claims owns any part of Antarctica.
Technically no-one owns any land in Antarctica. Various countries have staked claims in Antarctica but these have not been universally recognised and after the 1959 Antarctica treaty, which essentially prevented any future claims, Antarctica's status has been pretty much unchanged - lots of people claim to own chunks of it but everybody else says they don't. You could say the Australians because they claim the largest chunk of it...
No. The Antarctic Treaty acknowledges territorial claims -- and holds them in abeyance, some of which overlap each other, and prohibits future claims. A claimant does not 'own' anything, but claims it.
There is land underneath the ice cap. Several countries have already claimed parts of Antarctica. If the ice all disappears the countries (if they still exist) will still have claims on the land beneath the ice.
Antarctica belongs to no country, yet it 'belongs' to governments representing 80% of the population of planet earth. Antarctica is governed by the Antarctic Treaty -- as is all of planet earth south of 60 degrees South Latitude. The treaty documents existing land claims as invalid and prohibits future land claims. The treaty dedicates the continent and that part of the earth to science.