This paper develops a new framework to analyze the relevance of hillslope with respect to channel processes in the generation of the hydrologic response at different scales. The dependence between basin response and geomorphic features of channels and hillslopes is analyzed through the mean and variance of travel times under simple but realistic dynamical hypotheses and within the framework of the rescaled width function. The distribution of travel times is also studied in association with variations of the fraction of saturated areas: with small values of the saturated fraction, the channel network controls most of the mean and variance of travel time distribution. Vice versa, when the basin is saturated, the properties of this distribution may be significantly affected by hillslope processes. These properties depend also on the basin size, with the role of hillslope processes becoming more important in the smaller basins. Furthermore, the average residence time is related to contributing area and drainage density through a simple expression which is shown to be consistent with previous empirical laws.