We consider a model for the formation of a river network in which erosion
process plays a role only at the initial stage. Once a global connectivity is
achieved, no further evolution takes place. In spite of this, the network
reproduces approximately most of the empirical statistical results of natural
river network. It is observed that the resulting network is a spanning tree
graph and therefore this process could be looked upon as a new algorithm for
the generation of spanning tree graphs in which different configurations occur
quasi-randomly. A new loop-less percolation model is also defined at an
intermediate stage of evolution of the river network.Comment: 10 pages, RevTex, 4 postscript figures, accepted in PR