Expansion beyond Europe was called for during colonisation to the new world Africa Asia and the Pacific, It started with Africa, the people their were preached to and adopted the Christian faith quite quickly, it expanded over the 20th century rapidly and is still the strongest national growth referring to the church.
The Diocese were already well established in North America as early as 1511, they flourished, as for south America the Missionaries were successful. Eventually more Christian migrants went to America and fed the growth of the Church there.
When the Expeditions into Asia commenced the Japanese adopted the church but were soon persecuted for years, eventually the church was secure after the atomic bombing of nagasaki and the government was overthrown by the US.
China didn't really adopted Christianity as the Christian culture clashed heavily with Chinese culture.
Australian Missionaries came with the first fleet to Australia. The migrants from other christian countries founded the church here in Australia.