In Connecticut, the law is very clear about abandoned vehicles. Apart from those rebuilding them or having them stored in enclosed areas "with four walls and a roof," all other vehicles abandoned will be towed by local authorities. After that, they will try to find the owner, and if they can't, they'll sell the relic at an auction, if the vehicle is estimated to be worth $500 or less.
After the sale is concluded, they'll do the math with the towing and storing. If the state spent more than it got, it will send an invoice to the owner they couldn't find (funny, right?). If they get more from the vehicle than that sum, they'll send a letter to the owner telling them that they can reclaim the difference within a year. Sound about right, coming from the state, isn't it?
More than a decade ago, some guy found a Porsche Targa in his barn with no title, no bill of sale, and no clue about how it ended up there. Moreover, the car had just 44,000 miles on the clock. He tried to do things the right way, and he was fortunate. DMV found the last registered owner, who was still breathing. He sent him all the papers, including the bill of sale, and the Porsche lived a second life. That Porsche was a gambling debt, and the former owner kept his promise.
The right way to do that was not that easy since the authorities could've taken the car. So, in order to get it, the owner should've issued an invoice for storage, announced a lien sale, and then take it. That's how some vehicles were saved and didn't go to the crushers. After many years, some abandoned vehicles were discovered, such as this Corvette C2 who begged for a second life.
While in some states there is still some debate regarding abandoned vehicles, which are not a top priority for governments, they make that very clear in Delaware. For short, if a vehicle, an RV, trailer, motorboat, or motorcycle is abandoned on your property, you can claim it. It might not be as easy as requesting a title and receiving it the next day by mail, but it is still clear.
First, the authorities have to inspect and determine if it was stolen. Then, they will track down the owner's address and try to get in touch with them. Finally, the petitioner has to post announcements in at least five public areas in the county where the petition is filled and in a newspaper, regardless of the vehicle owner's address.
"A court will enter a judgment in favor of the petitioner unless an answer is filed within 20 days after the date on which the notice was mailed." As usual, if someone will show up and claim the vehicle, then you'd better be prepared to invoice them for storage.
In Delaware, you have to bear in mind that a vehicle is considered abandoned only after a year, and if the owner doesn't answer the petition sent to them by certified mail. It might take longer, but cudos for making it very clear.