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The stellar mass-halo mass relation is a key constraint in all semi-analytic,numerical, and semi-empirical models of galaxy formation and evolution.However, its exact shape and redshift dependence remain debated. Several recentworks support a relation in the local Universe steeper than previously thought.Based on the comparisons with a variety of data on massive central galaxies, weshow that this steepening holds up to z~1, for stellar masses Mstar>2e11 Msun.Specifically, we find significant evidence for a high-mass end slope of\beta>0.35-0.70, instead of the usual \beta~0.20-0.30 reported by a number ofprevious results. When including the independent constraints from the recentBOSS clustering measurements, the data, independent of any systematic errors instellar masses, tend to favor a model with a very small scatter (< 0.15 dex) instellar mass at fixed halo mass, in the redshift range z < 0.8 and forMstar>3e11 Msun, suggesting a close connection between massive galaxies andhost halos even at relatively recent epochs. We discuss the implications of ourresults with respect to the evolution of the most massive galaxies since z~1.

On the intermediate-redshift central stellar mass-halo mass relation, and implications for the evolution of the most massive galaxies since z~1