  We use the COSMOS2020 catalogue to measure the stellar-to-halo mass relation
(SHMR) divided by central and satellite galaxies from $z=0.2$ to $z = 5.5$.
Starting from accurate photometric redshifts we measure the near-infrared
selected two-point angular correlation and stellar mass functions in ten
redshift bins and fit them with an HOD-based model. At each redshift, we
measure the ratio of stellar mass to halo mass, $M_*/M_h$, which shows the
characteristic strong dependence of halo mass with a peak at $M_h^{\rm peak}
\sim 10^{12}\, M_{\odot}$. Our results are in accordance with the scenario in
which the peak of star-formation efficiency moves towards more massive halos at
higher redshifts. We also measure the fraction of satellites as a function of
stellar mass and redshift. For all stellar mass thresholds the satellite
fraction decreases at higher redshifts. At a given redshift there is a higher
fraction of low-mass satellites. The satellite contribution to the total
stellar mass budget in halos becomes more important than centrals at halo
masses of about $M_h > 10^{13} \, M_{\odot}$ and always stays below by peak,
indicating that quenching mechanisms are present in massive halos that keep the
star-formation efficiency low. Finally, we compare our results with three
hydrodynamical simulations Horizon-AGN, Illustris-TNG-100 and EAGLE. We find
that the most significant discrepancy is at the high mass end, where the
simulations generally show that satellites have a higher contribution to the
total stellar mass budget than the observations. This, together with the
finding that the fraction of satellites is higher in the simulations, indicates
that the feedback mechanisms acting in group-and cluster-scale halos appear to
be less efficient in quenching the mass assembly of satellites, and/or that
quenching occurs much later in the simulations.
