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ABSTRACT The past decade has seen significant progress in understanding galaxy formation and evolution using large-scale cosmological simulations. While these simulations produce galaxies in overall good agreement with observations, they employ different sub-grid models for galaxies and supermassive black holes (BHs). We investigate the impact of the sub-grid models on the BH mass properties of the Illustris, TNG100, TNG300, Horizon-AGN, EAGLE, and SIMBA simulations, focusing on the MBH − M⋆ relation and the BH mass function. All simulations predict tight MBH − M⋆ relations, and struggle to produce BHs of $M_{\rm BH}\leqslant 10^{7.5}\, \rm M_{\odot }$ in galaxies of $M_{\star }\sim 10^{10.5}\!-\!10^{11.5}\, \rm M_{\odot }$. While the time evolution of the mean MBH − M⋆ relation is mild ($\rm \Delta M_{\rm BH}\leqslant 1\, dex$ for 0 $\leqslant z \leqslant$ 5) for all the simulations, its linearity (shape) and normalization varies from simulation to simulation. The strength of SN feedback has a large impact on the linearity and time evolution for $M_{\star }\leqslant 10^{10.5}\, \rm M_{\odot }$. We find that the low-mass end is a good discriminant of the simulation models, and highlights the need for new observational constraints. At the high-mass end, strong AGN feedback can suppress the time evolutionmore »
