Grant Deed and Title question

[Peggy Liu]

I am in the process of helping my parents put together their Living Trust.  One of the big questions is that the grant deed on their primary home has their two names.  However, the title to the property has our three names.  Does this mean that I need to fill out a form to put my name to the grant deed?  This property is in CA.  Will putting my name trigger property reassessment?  Btw, the grant deed is currently in joint ownership between my parents.  What is the best way to go about putting the house into the Living Trust without triggering any unneccessary assessments?