Is it contested? What do you mean by contested?

All claims are held in abeyance while the treaty is in force. http://www.ats.aq/e/ats.htm

Were it not for the treaty there would be conflicting claims -- especially Great Britain, Chile, and Argentina, which all have claims on the Peninsula. Not to mention the US, which doesn't claim anything, but notably has a station sitting squarely on the pole itself. In one sense, perhaps all this geopolitical maneuvering motivates the signatories to maintain the treaty.

If the treaty expires or is nullified, or if commercial extraction of natural resources becomes economically viable, then you might see some friction.

For now, it's the very model of international cooperation. The rest of the world should have it so good.