No genetic model can explain the variability in distributary network pattern on modern deltas. Here we derive scaling relationships for two processes known to create distributary channels and, with these laws, construct a simple model for distributary network evolution. The first process is mouth-bar deposition at the shoreline and subsequent channel bifurcation; the second is avulsion - the wholesale abandonment of a channel in favor of a new path. The former creates relatively small networks with power-law distributions of channel length; the latter generates relatively few, backwater-scale distributaries. Frequency-magnitude plots of channel length on natural deltas agree with theoretical predictions and show a clear separation in scale that reflects these processes: Mouth-bar distributary lengths scale with the width of the parent channel, and avulsive distributary lengths scale with the backwater length; intermediate channel lengths are relatively rare. Wave energy controls network topology by suppressing mouth-bar development, thereby preferentially eliminating smaller-scale distributaries.