Which European countries gained territory of the Ottomans? How?

France and Great Britain won most territories that had formerly belonged to the Ottoman Empire. The latter was one of the losing powers of World War One - a German ally - and the conflict had worn out the administration. British troops had occupied Syria, Palestine and Mesopotamia; there was threat of direct occupation by British, French and Greek forces following an armistice in 1918.

Negotiations took place in France and the Treaty of Sevres was finally signed in 1920. Disguised as a League of Nations mandate, the British and the French saw their control of Syria, Palestine, Jordan, Iraq and Lebanon ratified. Greece got Eastern Thrace and Ionia. Italy received the Dodecanese islands and a part of Anatolia. Armenian were given an independent state in Western Anatolia.

In Europe, there were more new countries being created than countries gaining land from each other. With Austria-Hungary and the Ottoman Empire both collapsing, their land was carved up into a bunch of smaller states. Off the top of my head: Czechoslovakia, Poland, Bulgaria, Romania, the Baltics, Yugoslavia.