Not to discourage further discussion, but this topic has been broached before. Examples:
https://www.reddit.com/r/AskHistorians/comments/1crpfs/was_antarctica_ever_claimed_by_a_nation/ (from /u/Squipper2013)
https://www.reddit.com/r/AskHistorians/comments/2oz33s/national_territorial_claims_in_antarctica_why_did/ (from /u/spikebrennan)
To learn about present international law regarding Antarctica, see the Antarctic Treaty System (http://www.ats.aq/e/ats.htm), which has been in force since 1961.
Edit: punctuation