I live in Chesapeake, Virginia and I haven't been able to find a reference as to what my legal options are when it comes to a neighbor's tree and my yard. I could only find a "general rule" for America that says one can trim the portions of a neighbor's tree that hangs over your yard, however you have to offer the trimmings to the neighbor if they want it.
Its a magnolia tree, which sheds leaves year round. Its hard to see in the picture below, but all those yellow spots in the green leaves are dead leaves about to fall. If I don't mow or rake at least every other week, my backyard looks like it's the middle of fall year-round. It also drops seed pods - similar to pine cones, but much denser - that get stuck in my lawnmower. The tree shades the ground near its trunk, so nothing grows there. There is roughly a 20 foot radius of dirt, leaves, and weeds that looks terrible. That bottom branch has grown significantly over the last two years and is staying low, which is causing the dead area to grow. The Sun rises from the right side of the picture, so the tree in front of the magnolia blocks much of the light. That means, the magnolia has to creep into my yard to get light.
As you can see, about half - and likely more - of the tree is over my yard. I would love to get rid of the tree entirely, to keep my yard from the constant rain of leaves and pods, but I don't think I can do that. If I were to trim off all the parts over my yard, I would expect the tree to die, which I think my neighbor would not be happy about. At the least, I could get rid of that bottom branch, but that wouldn't solve much of my significant annoyance with this tree.
What are my options?