Shanghai is a very popular supporting character (or artifact) in Touhou fan art depicting Alice.
Some comic artists give the doll a personality and feelings of its own, making it a "master doll" that helps control the lesser dolls. Others show it as Alice's primary magically-controlled "puppet". These points of view can be mixed, possibly to give an impression of Alice "debating with herself" through doll use, reminiscent of the way ventriloquists use puppets. Sometimes she/it is even depicted as lacking "doll" traits entirely, resembling a minigirl.
Another view is that Shanghai is a type or class of magical dolls rather than an individual doll. This is based on the fact that several Shanghai dolls are seen simultaneously in PCB.