All:

Yes, there is a written rule, or perhaps several rules or laws about a fan taking a bat that ends up in the stands. Just look to your local, state, and federal laws under theft. It is not your property, so if the team or any of their employees or agents determine they want their property back, they have the right to do so. It is their property, period. Just because there is no sign posted saying that you can't take the bat home doesn't mean it is yours. Is there a sign at Walmart that says you can't take things home without paying for it? No, because everybody knows that is theft.

Matt