  We present STEEL a STatistical sEmi-Empirical modeL designed to probe the
distribution of satellite galaxies in groups and clusters. Our fast statistical
methodology relies on tracing the abundances of central and satellite haloes
via their mass functions at all cosmic epochs with virtually no limitation on
cosmic volume and mass resolution. From mean halo accretion histories and
subhalo mass functions the satellite mass function is progressively built in
time via abundance matching techniques constrained by number densities of
centrals in the local Universe. By enforcing dynamical merging timescales as
predicted by high-resolution N-body simulations, we obtain satellite
distributions as a function of stellar mass and halo mass consistent with
current data. We show that stellar stripping, star formation, and quenching
play all a secondary role in setting the number densities of massive satellites
above $M_*\gtrsim 3\times 10^{10}\, M_{\odot}$. We further show that observed
star formation rates used in our empirical model over predict low-mass
satellites below $M_*\lesssim 3\times 10^{10}\, M_{\odot}$, whereas, star
formation rates derived from a continuity equation approach yield the correct
abundances similar to previous results for centrals.
