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If the owner purchased the restaurant equipment, then that equipment is still legally his, although you could petition the court to declare the property abandoned. Also, if you own the real property, you could charge the previous owner storage on the equipment, and the charges would probably be greater than the value of the equipment. So, if he ever returned, you could just hand him a bill and offer to settle it in exchange for the equipment.
As far as the DBA goes, that's just a license to use a name. It doesn't convey any other ownership rights. You can call the business whatever you want and relicense it whenever you want.
Hope this helps.
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