car is registered under dead dad

well it depends on where you live some states don't require a notarized bill of sale so you could just go ahead and have your mom or someone else sign his name.

or take death certificate with the executor and get the title transferred, was the car in his will?

Car would become part of the estate. The executor of the estate would have to transfer it to you (assuming you are not executor).

If your dad's estate is not subject to estate taxes (either because it is going to your mom or is under the limit in your state if it has an estate tax) it probably does not matter much but if it is, then you should make sure you handle the transfer to you as an estate expense\payment of an outstanding debt so it is not counted as part of the estate's total value for tax purposes (something you need to make sure the estate accountant\executor would understand). As long as you have records of the payments for the vehicle, that should not be difficult to do.

If the car is legally registered to your dad, then the insurance is also in his name. Are you listed as the driver of the car on that policy, even though it is his policy?

You need to discuss the insurance situation with the Executor as soon as possible. Laws vary by state, but in some situations an auto policy is cancelled immediately after the Primary Insured dies. Here in Georgia, a deceased person's auto policy will remain in effect until probate is over and it covers any one who drives the car during that time. But you need to find out how it works in your state to be sure the car is insured!

Even though it might seem like the easiest solution, do NOT insure the car in your name until ownership has been legally transferred to you in writing! Most insurance companies would sell you a policy in your name, but if you had an accident they would be within their rights to deny payment if they discovered you weren't the legal owner the car. You must have "insurable interest" (ownership stake) in order to legally insure a vehicle in your name.

I'm an insurance agent here in Georgia and making sure that a deceased person's estate is fully covered during the probate process can be very tricky! I've seen a house burn to the ground and insurance didn't pay a penny to the family because the had left the policy is their deceased dad's name after they inherited the house! They lose EVERYTHING!

If your dad owns the car but it is registered and insured in your name, then I wouldn't worry about it unless you are looking to sell it. Otherwise, you could simply have someone else sign his name as many states don't even require a notarized signature to transfer ownership.

Sorry about your loss. Get with whoever is handling his estate. Find out if anything is in his will about the car. Likely all of the assets transferred to your mom. If your mom is willing to let you have the car, than call up the office in your state where you register/title cars and ask them what the process is to have the car titled in your name. The executor of the state and your dad's death certificate will likely have to go to the office and file a form.

Car -> Father's estate

Estate goes through probate. Debt's in his name are paid from that. None? The estate (and your car) go to his widow.