Legal Question in Real Estate Law in North Carolina

As much time as you want. He is a tenant at will. There is no time period, but I would give him a reasonable time in a notice to vacate. I would tack a notice to the door or give him written notice personally. Depends on your relationship with him but you could be generous and give 30 days or less so and give 15 or even less than that. As a practical matter though, its really hard to just pack up and get a new place to live with only a week's notice.

For actual tenants, its 15 days for a lease of 1 year (unless its for nonpayment of rent in which case its 10 days) or less or 30 days for more than a year. This is not an actual tenant but a tenancy at will which means he can stay so long as you allow it.

You should indicate in the notice that the tenant's mother was permitted to stay there but as she is now gone, you desire to recover possession of the property so the tenant has x days to leave the premises or you will have to evict him.