Abandoned Property

Is there a law of abandonment between two parties on the title when one party leaves without reason leaving the other party in hardship trying tp pay all mortgage, tax,& insurance?

I had a renter move out last weekend without a notice and they trashed the house and they left a 10 by 12 out building on the property. I want to know how much time do they have to get the building before it becomes mine?

My roommate decided to take off with two months remaining on our lease. Her name and mine are both on the lease. She moved back to Connecticut and she left me with a bunch of furniture that she kept promising to get rid of. It's been three months and I gave her several deadlines to come get it or let me get rid of it. She refused both, what can I do?

what steps must be taken to get a judicial abandonment so I can sell equipment (tractors) left at our property for 19 months and have no viable means to collect storage? We received these units with approximately 50 other units that were moved to our location for safe keeping. They came from a dealership that went under. Most of the units came from manufacturers and we stored and sold some units for them and they picked up the remaining units and sent them to auction. However, the 2 pieces in question were used units and believed to have been either purchased for resale or sent to the dealer for repair. We have chased every known angle on these two units but cannot find anyone who knows why they were at the dealer for sure or who is the owner. The units have been on our yard now 20 months. The dealer that went under was well known and it was well publicized why he went under. Any local person would know of this and who to check with if they owned these units. Yes we do store machines for banks and others and we are storing the units. They take up needed space and we have to jockey them around often to make room for other units that belong to us. We have had to do maintenance and replace some parts on the units as well. We do not see a viable means to find any owner and collect storage, etc. and have them moved. We would like to know if we can be awarded the right to have them sold at an equipment auction to collect what is due and get them off our lot.

My Brother in law asked us to store a car engine for him back in 2004. We have asked him many times over the years to come and get it. He had since moved out of town and at one time said he didn't want it anymore. Now we want to sell it and get rid of it. He is threatening to sue us for theft of property, but still won't come get it. Is the engine considered abandoned property and can we sell it and keep the money from it?