In California:
1. A standard license plate remains with the vehicle when the title is transferred.
2. A personalized license plate can either stay with the seller or go to the buyer. The seller decides.

Please refer to the second question under FAQ on CA DMV's website:
[url=https://www.dmv.ca.gov/portal/dmv/detail/pubs/brochures/howto/htvr32]https://www.dmv.ca.gov/portal/dm ... chures/howto/htvr32[/url]