  The (standard) Brownian web is a collection of coalescing one- dimensional
Brownian motions, starting from each point in space and time. It arises as the
diffusive scaling limit of a collection of coalescing random walks. We show
that it is possible to obtain a nontrivial limiting object if the random walks
in addition branch with a small probability. We call the limiting object the
Brownian net, and study some of its elementary properties.
