TLDR: During World War II, different countries were interested in Antarctica, but there was no actual fighting. Nazi Germany, the United States, Chile, and Argentina all made claims to parts of Antarctica. Britain launched Operation Tabarin to establish a presence and protect its claim to the Falkland Islands Dependencies. The expedition set up bases and conducted research, which eventually led to the formation of the British Antarctic Survey. After the war, international cooperation increased with the International Geophysical Year and the Antarctic Treaty.

During World War II, Antarctica became a point of interest for several countries, but there was no actual combat on the continent. Nazi Germany organized an expedition in 1938 to preempt Norway's claim to Queen Maud Land, resulting in the establishment of a German claim called New Swabia. The United States also sent an expedition to Antarctica in 1939, establishing two bases before abandoning them. Chile and Argentina made their own claims in response to these activities.

In 1943, Britain launched Operation Tabarin in response to the German, Chilean, and Argentine activities. The objective of the operation was to establish a permanent presence and assert Britain's claim to the Falkland Islands Dependencies. The expedition set up bases on Deception Island, the coast of Graham Land, and at Hope Bay. The research conducted during Operation Tabarin continued in subsequent years and eventually led to the formation of the British Antarctic Survey.

After the war, competition among the claimant powers continued, as well as involvement from the United States and the Soviet Union. However, in the late 1950s, a cooperative international framework was established with the International Geophysical Year and the Antarctic Treaty. These agreements promoted scientific research and peaceful cooperation in Antarctica.

So, during World War II, different countries were interested in Antarctica, but there was no actual fighting. Britain launched Operation Tabarin to establish a presence and protect its claim to the Falkland Islands Dependencies. The expedition set up bases and conducted research, which eventually led to the formation of the British Antarctic Survey. After the war, international cooperation increased with the International Geophysical Year and the Antarctic Treaty.