Two situations typically arise. If the tree that falls into your property causes no damage but simply make a big mess, you may be solely responsible for all of the cleanup costs. It might be nice if the neighbour offered to help or cover some or even all of the costs, but there is no obligation on them to do so. If the fallen tree causes damage, such as landing on your car, or damaging the house your insurance policy may cover the physical damage, maybe even the cleanup costs. If the insurance company chooses, they may then seek to subrogate these costs by trying to reclaim them from the neighbour’s insurance company. If you had warned the neighbour about your concerns with their tree, and they had not taken any steps to deal with the tree that may complicate matters. However, merely warning a neighbour simply gives them actual notice. Conceivably, if they had it inspected by a properly qualified person, and nothing untoward was discovered, it may be that you don’t have a claim to pursue. Each case will be judged on the specific details.