I have a Hampton Bay remote ceiling fan that comes on by itself. I have removed the battery from the remote and it still comes on.

The receiver could be bad, or it could be picking up from another remote even at your neighbors'. Maybe try changing codes. There should be a row of tiny switches in the batter compartment of the remote and a matching set somewhere in the receiver. Maybe check the directions to find where. Change both sets of switches to another pattern. You want your switches the same as each other, but different from any others in range.

Thanks labman