ABSTRACT We study stellar property statistics, including satellite galaxy occupation, of haloes in three cosmological hydrodynamics simulations: BAHAMAS + MACSIS, IllustrisTNG, and Magneticum Pathfinder. Applying localized linear regression, we extract halo mass-conditioned normalizations, slopes, and intrinsic covariance for (i) Nsat, the number of stellar mass-thresholded satellite galaxies within radius R200c of the halo; (ii) $M_{\star , \rm tot}$, the total stellar mass within that radius, and (iii) $M_{\star ,\rm BCG}$, the gravitationally bound stellar mass of the central galaxy within a $100 \, \rm kpc$ radius. The parameters show differences across the simulations, in part from numerical resolution, but there is qualitative agreement for the $N_{\rm sat}\!-\! M_{\star ,\rm BCG}$ correlation. Marginalizing over Mhalo, we find the Nsat kernel, $p(\ln N_{\rm sat}\, |\, M_{\rm halo}, z)$ to be consistently skewed left in all three simulations, with skewness parameter γ = −0.91 ± 0.02, while the $M_{\star , \rm tot}$ kernel shape is closer to lognormal. The highest resolution simulations find γ ≃ −0.8 for the z = 0 shape of the $M_{\star ,\rm BCG}$ kernel. We provide a Gaussian mixture fit to the low-redshift Nsat kernel as well as local linear regression parameters tabulated for $M_{\rm halo}\gt 10^{13.5} \, {\rm M}_\odot$ in all simulations.