Originally Posted by uanj

Your question at the top asks if you go through Immigration in TPE. The answer is no, just follow the signs for international transit. As you are leaving China (or the parts under the jurisdiction of China Immigration) you will go through Immigration and exit China as moondog pointed out.

I have done exactly the same before, PVG-TPE-HKG on BR with no problem. However, once when the first flight was on CA, also part of a Star Alliance ticket, I was stopped by Air China at check-in. They pulled up some arcane law where travelers outbound from China cannot transit in TPE to a destination beyond Taiwan. Ultimately they let me board saying it was not my fault the ticket was issued. United on longer allows this routing but most RTWs are issued by LH who still do this. I doubt you will have a problem departing on BR.