Gift transfers of automobiles are covered by CA Vehicle Code § 5602 providing that owner who has made bona fide sale or transfer of vehicle and delivered possession to purchaser shall not be subject to civil liability for operation of vehicle thereafter by another when owner has made proper endorsement and delivery of certificate of ownership and delivered certificate of registration or has delivered to department of motor vehicles or has placed in the mail appropriate documents for registration of vehicle pursuant to the sale or transfer. Brown v. Fix (App. 2 Dist. 1978) 150 Cal.Rptr. 431, 86 Cal.App.3d 809.
What this boils down to is that if you have absolutely no writing concerning this arrangement, then you probably will not be keeping the vehicle at the end of the day.