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My brother wants to give his kids his share of our mutually held property without my permission. Is this legal?
Why wouldn’t it be legal? If you own something, one of the rights that comes along with that ownership is the right to sell or give away the thing you own.
There are some types of ownership that carry restrictions on transfer, most typically seen in partnership agreements or closely-held corporations and LLCs. But if you and your brother own the property directly, the presumption would be that it’s transferrable (unless there is some restriction somewhere).
However, all is not lost. If you don’t want to be co-owners with your niece/nephew, you can always buy them out, offer to be bought out, or sell the property and split the proceeds.