Legal Question in Real Estate Law in California

No. If the trust is to hold real property, a deed must be recorded from the trustor to the trustee, as trustee, even if that is the same person. So for example the deed would be from "John and Jane Smith to John and Jane Smith, trustees of the John and Jane Smith Family Trust dated July 11, 2001." The trust itself is not recorded.

The term "trust agreement" is a bit broad to give a categorical answer. Indeed, most trusts are not really even "agreements," since they are not usually negotiated and agreed upon between, say, the trustor and the trustee, or the trustor and the beneficiary. A typical living trust does not get recorded, and probably could not be recorded under the recording statutes even if the trustor or her attorney wanted to record it. It is conceivable that some special-purpose instruments could bear the title "Trust Agreement" and be recordable, but that would be very unusual. Similarly, wills are not recorded.