There is another strategy for dividing the space called point quadtrees (p quadtrees) which divides the regions at the point you are inserting. This gives an upper bound of the tree depth as the number of nodes inserted, which is still undesirable. To fix this, you have to choose the correct order for point insertion to obtain a well balanced tree with log_4(n) height.
It seems like you could balance as you went along in a similar fashion to balanced binary trees such as b-trees or AVL trees.
It seems like you could balance as you went along in a similar fashion to balanced binary trees such as b-trees or AVL trees.