Someone dies. He or she had a car. A car nice enough to keep. You are the only heir. The estate doesn't need probate for whatever reason.
First, determine if there is an existing note on the car. If there is a note, you will want to continue to keep paying the note until you can transfer title into your name.
Second, make sure there is insurance on the car.
Third, complete this form at the DMV called Affidavit for Transfer without Probate, California Titled Vehicles or Vessels only. You will want to go to your local DMV to file this form and ensure that title will now be in your name.
This form is part of the small estate affidavit procedure permitted by California Probate Code Section 13100, et. seq. When you complete and sign the Affidavit, you are stating under the penalty of perjury that you are the rightful heir, the estate is less than $100k, probate is/will not be opened and at least 40 days have elapsed since decedent died.
Last steps, call the car note holder and see if you can continue to pay on the note or if you need to do something. Each lender is different. Try to be nice, eh? And then call the insurance company again to cancel the decedent's insurance policy and re-insure the car under your own insurance policy.