AbstractThe performance of multiple empirical statistical downscaling (ESD) methods was assessed for simulating daily precipitation during 1979–2017 over southeastern South America (SESA), a region where extremes are remarkable. Meteorological stations were used as reference and three gridded precipitation products were included to account for observational uncertainty. The set of ESD models involved different configurations of the analogue method (ANs), deterministic and stochastic versions of neural networks (NNs) and generalized linear models (GLMs) and circulation‐conditioned GLMs (GLM_WTs). The years with the largest number of extreme events (wet years) were calibrated separately. The spatio‐temporal variability of extremes was assessed by analysing their intensity, spatial extent, frequency and interannual variability. An overall good performance of the ESD models was found for several aspects of daily precipitation. ESD performance dispersion was usually contained in the observational spread. No particular model configuration was found to perform best in all aspects, indicating the advantage of considering a multi‐model ensemble. The ANs tended to follow the stations, satisfactorily simulating daily precipitation and its extremes. The deterministic GLMs strongly underestimated precipitation estimates and were not able to represent extreme frequencies and intensities, but this was alleviated by employing a stochastic version of the method. Furthermore, the use of weather types to condition the GLMs (GLM_WTs) considerably improved model performance, particularly for the annual cycle and the spatial structure of extreme precipitation. The NNs adequately reproduced the spatial behaviour and intra‐annual variability of extreme precipitation, although they underestimated its intensity in their deterministic version. An analysis of the regional time series of extremes showed consistency among datasets and evidenced the influence of the ENSO teleconnection on the wet years, which were commonly well‐simulated by the statistical models. ESD models presented good skills in simulating a wetter climate over SESA, which is of particular importance in a climate change scenario.