Below is a short list of rain forests for the continents you requested.
ASIA. The Malaysian Rain Forest is the largest on the continent. There are also rain forests in the islands of Indonesia. Others can be found in Japan, China, Taiwan, Korea, Iran, Azerbaijan, Turkey, Georgia and Russia.
EUROPE. The Bialwieza Forest is a primeval habitat located in northeast Poland. Smaller rain forests can be found in Ireland, Scotland, Norway and in the Balkans.
SOUTHERN AFRICA. The Congolese Rain Forest along the Congo River Basin is the largest in Africa. The Knysna-Amatole coastal forest can be found in South Africa.