From my brief research, the rules regarding trees seem a little crazy - if my neighbor's tree has branches extending into my yard, even if they pose a risk or nuisance, I can cut them, but at my own expense. More importantly, f the roots from his tree extend into my property, causing actual damage, it seems that remedying the problem may still have to be at my expense - and I still have to be careful not to damage the tree - if the tree gets damaged, I could be responsible to pay!
Any knowledge/experience/thoughts?