The effects of erosion, avalanching and random precipitation are captured in a simple stochastic partial differential equation for modelling the evolution of river networks. Our model leads to a self-organized structured landscape and to abstraction and piracy of the smaller tributaries as the evolution proceeds. An algebraic distribution of the average basin areas and a power law relationship between the drainage basin area and the river length are found.

9 pages, Revtex 3.0, 7 figures in compressed format using uufiles command, to appear in Phys. Rev. Lett., for an hard copy or problems e-mail to agiacom@iff042.iff.kfa-juelich.de