Re: What happens if
If it grew in your yard its yours, there's many cases of fruiting vines growing along boundary fences and claiming ownership of the other side of the vine would just be infeasible, likewise if one person destroyed the vine on their side (effectively killing the entire plant) that's just unfortunate for the other person.
Law isn't a matter of what's fair but rather what works for society.
Poisoning the roots of the hypothetical apple tree would be incredibly spiteful but as long as you don't hurt anyone they can't really charge you with anything, likewise you could extend your house in a way that puts the tree in the shade and as long as you have council approval for the construction you're entitled to do it.
Of course starting a "who can be more spiteful" competition isn't a good idea.
Deadlier, Sillier and more Perverted.