The people whose backyard has the tree trunk has the responsibility of cutting the tree trunk. If the branches are hanging over your backyard, then you can cut them.
<h3>What are the property rights of trees?</h3>
If the tree trunk is in both of the property, you and your neighbor, then both are the owner of the tree.
If the branches of the tree of your neighborhood came into your backyard, then you have the right to cut them.
Thus, the people whose backyard has the tree trunk has the responsibility of cutting the tree trunk. If the branches are hanging over your backyard, then you can cut them.
Learn more about property rights of trees
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