In CA the only thing that matters is what's on the DMV system. If the vehicle is being sold within the same state it simplifies everything. They look on the system and see who the owner is and the paperwork has to match. If there's no physical title the owner (on the system) can fill out forms to make the transaction. If the vehicle is from out of state (out of CA) there HAS to be a physical title because they can't check it on the system, they're not linked. I would assume it would be similar in other states but your state's DMV is the only one that can answer that. If you want to be safe, go to your DMV and ask them what they need for paperwork for you to register it in your name. They should give you the forms with the steps highlighted.
If there is no physical title there may be a way to run a lien and get ownership that way. Again, check with local laws, that's all that matters.
