AbstractLow flows result from the interplay of climatic variability and catchment storage dynamics, but it is unclear which of these variables is more relevant for explaining low flow spatial patterns. Here, we develop a new conceptual model that integrates process‐based hydrological knowledge with statistics and test it for 1,400 Brazilian catchments. Through comparative hydrology, we isolate the low flow generating mechanisms and estimate their components using linear model trees. The model explains 58% of the spatial variance in 7‐day minimum annual flows (Qmin) based on climate and catchment characteristics. The primary Qmin controls depend on the spatial scale of analysis. Catchment characteristics govern Qmin up to the continental scale (107 km2), where their relative importance matches that of climate. At subcontinental scales, catchment characteristics are twice as important as climate in predicting Qmin, suggesting that low flows are governed by the catchment's capacity to attenuate the climatic variability through water storage. Geological properties are the most important catchment characteristics, particularly bedrock type, lithology and topographic slope, determining streamflow recession rates in the dry season. Soil properties, primarily soil class and depth, are half as important as geology. Climate impacts Qmin mainly through mean annual rainfall minus evaporation, representing the potential groundwater recharge, while dry‐season length has the lowest impact. These results hold mainly for highly seasonal and snow‐free climates. Low flow hydrology that combines statistics with process understanding offers a promising framework for understanding regional low flow generating mechanisms and could support other estimation models than that presented here.