Dispersion of tracers in random network is considered. Network models of natural media here include: i) channel networks, possibly of fractal nature, whose geometrical characters have recently attracted interest in hydrological literature; and ii) network models of porous media. For a random tube network exact rules are derived for tracer motion under the combined action of molecular diffusion and heterogeneous convection, which allow the calculation of first-passage time distribution of the tracer at fixed locations. The latter are connected to the dispersive character of the microdispersion processes which are related in a rational manner not only to the heterogeneity of the convection field but also to the geometrical features of the network. It is shown that the formulation of the transport for relevant hydrological processes at different scales can be viewed under a unifying approach of kinematic nature. In particular, we show a significant characterization of the hydrologic response for Hortonian channel networks.