I assume you are also not paying anything for the home. That should exempt it from the transfer taxes and from reappraisal and reassessment. Counties differ in their rules for claiming exemptions from transfer taxes (collected by the recorder) and from reassessment under Prop. 13 (a county tax collector function), so if you go through with this deal, inquire at those two offices before recording your quitclaim.
Now, let me give you some reasons why what you're proposing to do might not be such a good idea.
First, your mother's loan probably has a "due on sale or transfer" clause, and when the lender finds out it has changed hands, it could accelerate the loan -- make it immediately due and payable in full. So, review the terms of the loan, and if it restricts or prohibits the borrower from selling or giving away the property without the lender's permission (or, alternatively, refinancing or payong off the loan), try to get permission. Many lenders will allow a change of owners upon payment of a small application or processing fee.
Next, if you acquire the home as a gift now, you will be taking on its original cost basis going back to when your mother (or parents) acquired it, maybe decades ago at a very low price. When you sell it, you would then have a relatively large capital gain - the difference between the cost basis and the selling price. You'll pay capital gains tax, currently 15% but likely to rise. This can be many tens of thousands of dollars. On the other hand, if you were to inherit the house (by will or via a trust), the IRS recognizes what is called a "stepped up basis" - the fair market value at the time of inheritance. Because your cost basis will be higher, your taxable gain is smaller and your tax may be close to zero. See a tax advisor for details. Your mother might also have a gift-tax liability.
Finally, I always advise people not to give away property to try to keep assets away from creditors or potential creditors like a lawsuit plaintiff or Medi-Cal. Transfers of real estate at below fair market value are very obvious to creditors and can be attacked as fraudulent and set aside by a court, leaving both the donor and the donee potentially liable for damages in addition to loss of the transferred property.