The hydrologic response of a channel network is defined by decomposing the process of runoff formation into two distinct contributions, one accounting for the mechanisms of travel time within individual reaches (hydrodynamic dispersion), and the other accounting for the morphology of the network structure (geomorphological dispersion). Exact Laplace transforms of first passage time distributions at the outlet of a network are obtained by a consistent approximation of travel time distributions through individual reaches. The moments of such distributions are obtained analytically in the general case. Closed-form first-passage distributions are obtained in the particular case of basin-constant hydrodynamic dispersion. The variance of the resulting travel time distributions is shown in this paper to be made up of two additive contributions corresponding to the two dispersion mechanisms considered. The geomorphologic dispersion coefficient is shown to depend on the ratios of bifurcation, length and area of the network suggesting that, at the scale of an organized network, heterogeneities other than those related to the convection field shape the dispersive character of transport. In particular, a significant application of the general solution to Hortonian channel networks suggests that models based on accurate specification of the geometry and the topology of the network and a simplified dynamics capture the foremost features of the travel time distributions in a broad range of dispersivities within individual reaches.