A well-placed tree can benefit both you and your neighbour, bestowing shade, beauty and privacy upon both your properties. However, as trees grow, their root systems, as well as branches, can sometimes encroach upon a neighbour's property. When this happens, it is up to you as the tree-keeper to take action to ensure your tree does not pose a risk to your neighbour and their property.
According to the Herald Sun newspaper, from 2009 to 2012 the Victoria Dispute Settlement Centre took 53,000 calls primarily concerning disputes between neighbours over bad behaviour, fence issues and trees.
Whether you planted the tree or not is of no concern. The fact that it is on your property makes it your legal responsibility. Therefore, if your neighbour has informed you of an issue, it is up to you to do something about it before the situation escalates.
If your neighbour complains that your tree's branches are invading their property, have those branches trimmed. Otherwise, your neighbour has a legal right to trim back those branches up to the boundary dividing your two properties.
Likewise, if your tree's branches have been shown to be a possible hazard in the event of a storm, you are liable to pay for any damages should those branches damage your neighbour's property.
Keep your trees well-pruned to avoid this issue.
In the event that your tree's root system is causing a neighbour's fence to buckle or a fence post to shift, they have the right to cut those roots back.
However, as the tree-keeper, if you notice that your tree's roots are damaging a neighbour's property, you should offer to cut the roots on their property yourself.
Some trees, such as the gum tree and the Norway maple, shed branches. Fruit trees too can drop seeds and fruit into a neighbour's property, potentially attracting pests like wasps.
Again, because your tree is affecting your neighbour's enjoyment of their yard and possibly creating a hazard, you should take the initiative and offer to remove those branches.
Otherwise, your neighbour has the right to remove those branches.
If your tree has grown to such an extent that it has begun to block your neighbour's view, or deprive them of sunlight, they may have a legal right to do something about it. However, rather than cause a dispute over it, because you may likely lose out in the end anyway, you should arrange to have your tree pruned or cut back in order to reduce its canopy.
As the tree-keeper, ensure you keep your trees pruned and maintained to avoid disputes such as these. Meet with your neighbours and discuss the issue. Nobody likes to remove trees if they don't have to, but angry neighbours may no longer see things this way. Before things get out of hand, arrange for a tree specialist to come out for regular tree lopping on your property.