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Consider the d-dimensional lattice Z^d where each vertex is ``open'' or  ``closed'' with probability p or 1-p, respectively. An open vertex v isconnected by an edge to the closest open vertex w such that the dthco-ordinates of v and w satisfy w(d)=v(d)-1. In case of nonuniqueness of such avertex w, we choose any one of the closest vertices with equal probability andindependently of the other random mechanisms. It is shown that this randomgraph is a tree almost surely for d=2 and 3 and it is an infinite collection ofdistinct trees for d\geq4. In addition, for any dimension, we show that thereis no bi-infinite path in the tree and we also obtain central limit theorems of(a) the number of vertices of a fixed degree \nu and (b) the number of edges ofa fixed length l

Random oriented trees: A model of drainage networks