The central limit theorem for Euclidean minimal spanning trees I I

Let Xi:i.1 be i.i.d. with uniform distribution [.1/2,1/2]d,d.2, and let Tn be a minimal spanning tree on X1,.,Xn. For each strictly positive integer ., let N(X1,.,Xn;.) be the number of vertices of degree . in Tn. Then, for each . such that P(N(X1,.,X.+1;.)=1)>0, we prove a central limit theorem for N(X1,.,Xn;.).