Actually, they'd be in legal trouble if they didn't give you the branches back - you can charge them with theft if they don't.

You can ask them to give you a warning though, but they don't have to.
yup. DF works for a tree company, if the branches they are paid to remove is growing from the neighbours tree, they cut it and "return" the cut branches. works out cheeper for the person paying for the removal of them to.