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We present the global and regional hydrological sensitivity (HS) to surface temperature changes, for perturbations to CO2, CH4, sulfate and black carbon concentrations, and solar irradiance. Based on results from ten climate models, we show how modeled global mean precipitation increases by 2-3% per kelvin of global mean surface warming, independent of driver, when the effects of rapid adjustments are removed. Previously reported differences in response between drivers are therefore mainly ascribable to rapid atmospheric adjustment processes. All models show a sharp contrast in behavior over land and over ocean, with a strong surface temperature-driven (slow) ocean HS of 3-5%/K, while the slow land HS is only 0-2%/K. Separating the response into convective and large-scale cloud processes, we find larger inter-model differences, in particular over land regions. Large-scale precipitation changes are most relevant at high latitudes, while the equatorial HS is dominated by convective precipitation changes. Black carbon stands out as the driver with the largest inter-model slow HS variability, and also the strongest contrast between a weak land and strong sea response. We identify a particular need for model investigations and observational constraints on convective precipitation in the Arctic, and large-scale precipitation around the Equator.