  Observational systematics complicate comparisons with theoretical models
limiting understanding of galaxy evolution. In particular, different empirical
determinations of the stellar mass function imply distinct mappings between the
galaxy and halo masses, leading to diverse galaxy evolutionary tracks. Using
our state-of-the-art STatistical sEmi-Empirical modeL, STEEL, we show fully
self-consistent models capable of generating galaxy growth histories that
simultaneously and closely agree with the latest data on satellite richness and
star-formation rates at multiple redshifts and environments. Central galaxy
histories are generated using the central halo mass tracks from
state-of-the-art statistical dark matter accretion histories coupled to
abundance matching routines. We show that too flat high-mass slopes in the
input stellar-mass-halo-mass relations as predicted by previous works, imply
non-physical stellar mass growth histories weaker than those implied by
satellite accretion alone. Our best-fit models reproduce the satellite
distributions at the largest masses and highest redshifts probed, the latest
data on star formation rates and its bi-modality in the local Universe, and the
correct fraction of ellipticals. Our results are important to predict robust
and self-consistent stellar-mass-halo-mass relations and to generate reliable
galaxy mock catalogues for the next generations of extra-galactic surveys such
as Euclid and LSST.
