The main wealth-type tax in California is the property tax
. This tax was the subject of a state constitutional amendment, which passed in 1978, called Proposition 13
. It is a major source of revenue as you can see from the first link. Generally, there's not too much grumbling about it at this point because it only goes up 2% a year, as per the Prop. 13 revisions, and funds generally supported local services. There's lots of pros and cons in the second link.
A general wealth tax sounds like a really bad idea for lots of reasons.