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There are no options to obtain ownership of the vehicle outside of the judicial process
(You cannot take title to someone else's property without judicial process).
However, if the friend who would like to deal with this car that has been left behind wishes to deal with the matter, he can send the ex-girflriend a notice to recover her vehicle within a specific period of time (such as 15 days of the date of the letter). If she fails to recover the vehicle, he can then file a court action to eject the vehicle and to charge for the costs of towing, etc.
But he does not automatically get title to the car.
Your friend can notify the owner of the car, and even contact a tow company to determine specific tow rights (this gets very complicated because I would hazard that your friend allowed her to store the vehicle there - so most tow companies are going to be reluctant to tow without a court order - which is why I suggested a court order above).
But your friend still does not get title to his ex's car - if it ends up getting towed, he can bid on it at public auction.