The root as well as the trunk of the tree is in the neighbour's boundry/house. 70% of the tree's fruit is on neighbour's side and 30% is on my side.
This means that the tree is owned by your neighbor -legally speaking, check your local governance on who is responsibility the tree would be.
Unless you have a understanding between you and the neighbor that the tree is owned by you both, taking fruits from it is considered stealing.
There are exceptions when it comes to trees that extend outside of the property line. The prophet PBUH said:
رواه أحمد وابن ماجه أن رسول الله صلى الله عليه وسلم قال: إذا أتى أحدكم حائطاً فأراد أن يأكل فليناد: يا صاحب الحائط ثلاثاً فإن أجابه وإلا فليأكل، وإذا مر أحدكم بإبل فأراد أن يشرب من ألبانها فليناد يا صاحب الإبل أو يا راعي الإبل فإن أجاب وإلا فليشرب...
It was narrated that the Prophet PBUH said: If someone came into a wall and he wanted to eat from it, he is to call the owner three times, if he doesn't answer to eat, and if someone passes by a flock of camels and wanted to drink from it to call its owner if he doesn't answer he can drink.
According to the following Fatwa (see source), it is not allowed unless you ask for permission. If you are bothered by the branches in your property you can ask you neighbor to trim it down and insure it doesn't happen.
Source (in Arabic): http://fatwa.islamweb.net/fatwa/index.php?page=showfatwa&Option=FatwaId&Id=51744