Estimating mean flow or low flow and flood percentiles remains a difficult task of modern hydrology, especially on ungauged catchments. When establishing determination methods, one problem lies in the treatment of outlier catchments, i.e. those catchments that do not fit the expected law or estimation relationship. What can we learn from these outlier catchments? This study investigates this issue by mapping characteristic flow estimates over a set of 920 gauged catchments spread in France. We used simple regression relationships to estimate mean flow, the 10-year flood and the 5-year minimum monthly flow from several catchment physical and climatic descriptors. While these relationships yield satisfactory results at the national scale, large errors could be found on a limited number of catchments. Mapping the errors obtained by applying these relationships gave insight on the location of outliers and on possible sources of errors. Regional patterns could be observed. Interestingly, outlier catchments are not systematically the same for the three target variables. As could be expected, the definition of a hydrological monster may come from the view point it is looked at.