We characterize average slip distributions on earthquakes beyond their individual heterogeneity. For that, we analyze a large number of seismic slip distributions both measured at the surface after earthquakes (44 profiles) and derived from slip inversion models (76 models). Investigating the overall shape of these slip profiles, we find that they are roughly triangular both along strike and dip, and most of them (70--80%) are asymmetric. Long linear slopes and high slip gradients therefore are the key ingredients to describe earthquake slip profiles. The scaling relations between maximum displacement and length (or width) suggest furthermore that the triangular slip profiles are self-similar. Such slip patterns make earthquakes dominated by one major zone of maximum slip hence one major asperity. Analyzing the position of hypocenters with respect to these asperities, we find that earthquakes nucleate at a distance from them that averages 20--30% of their total length. Compiling observations on 56 earthquakes, we show that this distance (i.e., the asperity size) is structurally defined. We then compare the earthquake slip profiles to cumulative slip profiles measured on long-term faults of various ages and sizes and find that all profiles have a similar shape, triangular and asymmetric. Hence combining data for a large number of earthquakes leads to point out average, generic characteristics of the coseismic slip that are similar to those that emerge from the accumulation of events with time on a single fault. This suggests that these characteristics result from robust physical properties.