‘If the roots or branches of your tree encroach on your neighbour's land, they can cut them back to the boundary line. In law, this is called "abatement". If they don't want to do this themselives, they can ask a district court for an order for the trimming or even removal of the tree.
However, if the tree is not causing harm or loss of enjoyment, abatement may be their only remedy. If they choose this option, they must do no more than is necessary to abate the nuisance. No unnecessary damage should result, and they should not trespass on their property, and not create any other problems for you. They must not poison the roots or spray the tree with herbicide, as the consequences would extend beyond their property. If they are cutting out part of the tree's roots, take care not to undermine the stability of the tree or the ground around it.
Cuttings and fruit belong to the tree owner. They can put them back on your property, taking care not to cause any damage, or ask for them to be removed.’
Who pays?
‘If they have incurred costs in cutting back the roots and branches on their side of the boundary, they probably will not be able to claim them back from the tree owner.
But if the roots of your tree have damaged their drains or a branch falls on their house, you will probably have to pay. Even if the damage results from forces outside your control, you may still be liable if they could have been expected to know the tree was unsafe, and did not take reasonable steps to make it safe.’