My neighbour has a wire fence and i have to keep cutting back there bushes / ivy, i asked if they would do something about it as i dont think it should be my responsibility to maintain their garden, do they have a responsibility to keep it maintained.
What grows over you side of the fence is your responsibility so you can cut back as far as the fence only and any cuttings are your neighbours and may be put back over their side, tree branches and any fallen fruit are theirs also.