Now I know this has been done over and over and over, but I've just got a couple of thoughts about this idea of world Chinese dominance in the Middle Ages having been possible if Zheng He hadn't been screwed over by the eunuchs.
My first thought is, if the Chinese had got to Europe would they really have achieved any kind of dominion over the Europeans? Or would they just have provided a ready point of trade for the Europeans while they competed amongst themselves and reached greater levels of power? Would it have been in the Chinese mindset to establish themselves as rulers of Europe? Vassals, maybe.
My second thought is, would the Chinese have any interest in building colonies? Would they have settled the New World, sponsored the creation of cities in the America, Australia, South Africa? I can see why the Chinese lower classes would have an interest in doing so, but would the eunuchs/bureaucrats/temple faction/emperors have put in the money for these settlements, when they had so much land back home?
Resident experts?