My name is ***** ***** I'd be happy to answer your questions today. I'm sorry to hear about your situation.
You're both a partially right, but you're also both partially wrong.
The house belongs to him. If he is allowing you to live in it with the children, then you have the same legal rights as a tenant. Any amounts you're paying for the property are just considered rent. A person does not gain any right to ownership
of a house simply through living there a long time with the owner's consent. That means that he's legally allowed to ask you to leave by giving you 30 days written notice. N.H. Rev. Stat., Section 540:3.
He cannot enter at will. He cannot enter at all, other than to make necessary repairs, with your permission, or in an emergency. A tenant has the right to the exclusive use and enjoyment of the premises. Now that he's moved out, if he enters without your permission, he's trespassing. You can actually claim that whatever he left behind is abandoned if it's been more than a couple of months, but he needs a court order to go in and enter. Keep in mind, though, that if he sues, the judge is going to order you to pay him the value of his items - so you'll be stuck with his stuff, and you'll have to give him money. Depending on what the items are and if you're also using them, consider if you'd rather do that than arrange for a pickup.
He is welcome to sell the house. Your right to live there transfers to the new owner, and they can serve you with a notice to leave at any time. Alternatively, they'd be allowed to give you 30 days notice that they were going to charge you market rent if you'd like to stay in the premises.
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