Where did the piñata come from?

Virtually every month we celebrate the birthday of a relative’s kid with the traditional “kids hit the piñata until it breaks and treats and/or presents fall down” bit.

Looking at some websites for the history of the piñata, I noticed that some mentioned an Italian origin (The Italian word ‘pignatta’ means “fragile pot.”). But other sites claim that China (maybe) invented it.

Well, I was not able to find more conclusive sources so: since the SDMB has a world wide reach, I ask our fellow dopers for more info to see if we can pinpoint the origins of this tradition, quickly becoming a staple of birthdays in the USA too.