Legal Question in Real Estate Law in California

You do not provide enough information to answer your question. If, however, your mother transferred title to the property into a Trust [which a Living Will is], then ownership is in the Trust to be distributed as the trust documents provide. A Quit Claim deed merely states that the person receiving the Deed has a superior title to the person giving it; it hasfor some time been used to transfer title to property. But if your mother had no title to the property when she gave you a quit claim deed, then you have nothing.

It is a "quit claim" deed and not a "quick claim" deed. A quit claim deed quits all of the owner's claims to the property to the person receiving the deed, without any warranties.

Assuming that the quit claim deed was validly executed, when your mother was competent, you have the right to the property. The property listed in the will that was quitclaimed has been adeemed by extinction.

Wills can be changed and their effectiveness altered by things the testator does up until death, at least while they still possess legal capacity. Giving away or selling property prior to death takes it out of the will, because a person cannot bequeath what they do not own. As Mr. Roach indicates, this process is called ademption. "Ademption is a term used in the law of wills to determine what happens when property bequeathed under a will is no longer in the testator's estate at the time of the testator's death. For a devise (bequest) of a specific item of property (a specific gift), such property is considered adeemed, and the gift fails. For example, if a will bequeathed the testator's car to a specific beneficiary, but the testator owned no car at the time of his or her death, the gift would be adeemed and the aforementioned beneficiary would receive no gift at all." (quoted from Wikipedia)

So, the quitclaim deed if properly executed and delivered will prevail.

If it was a valid deed, it transferred the property to you prior to death. Then the will disposes of whatever else was left in the estate.