Packing plane spanning trees into a point set

Let P be a set of n points in the plane in general position. We show that at least ¿n/3¿ plane spanning trees can be packed into the complete geometric graph on P. This improves the previous best known lower bound O(n). Towards our proof of this lower bound we show that the center of a set of points, in the d-dimensional space in general position, is of dimension either 0 or d