After Buddha died, in the first three centuries, Buddhism spread along India, surpassing even Hinduism, the traditional religion of the country. Following India, many Asian countries, including Tibet, Thailand, Sri Lanka, China, Myanmar. Buddhism is actually the official religion of Cambodia.
The thing is, Buddhism learned how to live peacefully with other religions, be as it may, they mixed themselves into many variations of Hinduism and Buddhism, Taoism... Theravada Buddhism appears to have more followers and adepts than others segments, Cambodia, Thailand, and Sri Lanka are examples of Theravada Buddhists. China declares itself an atheist country, therefore it is more difficult to consider the Buddhist citizens of China.
