I hope you meant the three branches in the sense of practice session. During a practice session, the three branches are.
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This could vary depending on what level you are talking about. Some consider the three branches as Okinawan, Japanese and Korean. Others look at the three main branches of Okinawan karate, where it originated, as Shorin Ryu, Shuri Te and Naha Te.
There are two primary schools in Japan. Shotokan was established in the 1930's by Gichin Funikoshi. Shorinji-kemp was started shortly after World War II.