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Yes, the same rules discussed above apply to your neighbor: They can trim one of your trees as long as they’re only cutting the portion that extends into their property. Your neighbor is not allowed to access your property without permission, nor can they cut past the property line. 

The cost of trees varies massively based on the size of the tree and the species. A small Colorado spruce can cost as little as $30, but a golden rain tree of the same size can cost $90. Large trees can cost $1,500 or more, depending on their species and height.

Depending on the severity of the damage, a tree might continue healing for years after a split or a break. Saplings can usually bounce back in the spring in one or two seasons, but larger trees might take a few years to regain their former strength. If your tree is showing strong growth and is not dropping limbs, you can consider it healed after the first two seasons.

Whether tree roots will continue to grow after a tree has been cut down depends on the species. Some tree roots will eventually die because they can no longer get nutrients through photosynthesis. However, other species that reproduce through root sprouts can continue to grow and produce new sprouts for seven years or more. For example, the roots of elms, ficus, and willows tend to regrow aggressively, while the roots of pines, oaks, and maples will typically die. To determine if a root system is still active, look for new sprouts on the old trunk, stump, or any exposed roots.