Answer: If you decide to remove the laurel, you can have someone cut it off at ground level and then dig out the roots. If you leave the roots there, they will probably sprout new stems. That might not be such a bad idea - perhaps your neighbor will appreciate the plant more when it is small. As it grows, you can keep it pruned so it stays inside your property line and your neighbor will have no reason to come over and cut it back.
Best wishes with your garden!
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