Under conditions of unsaturated flow, others have shown experimentally that fracture intersections can direct flow to a single exiting fracture. In addition, they have been found to gather water from above to release as a pulse below. We formulate a simple model where these two behaviors are embedded within a network. With slow steady inflow distributed randomly along the top of the network, the system self organizes to form avalanches of water that can penetrate to great depths. When all intersections split their outflow, flow diverges with depth and develops into a self-organized dynamical state where the distribution of avalanche sizes follows a power-law over many decades. As the fraction of intersections that direct outflow singly is increased, spatial structure passes from divergent through braided to a fully convergent, hierarchical flow regime where avalanche size is minimized along one-dimensional slender pathways.