Relationship between BH mass and stellar mass of the host galaxies in the Cl13 (upper panels), D9 (central panels), and CBox simulations (lower panels). Each column contains the results obtained with a different BH dynamics prescription: DYNFRIC (left), DYNMASS (central), REPOS (right). The diamonds refer to the BHs associated with the main halos while circles correspond to sub-halos belonging to halos more massive than 10¹⁰ M_⊙ Diamonds and circles are colour-coded according to the distance between the sub-halo centres and the associated BHs. For comparison, we also plot observational data from Gaspari et al. (2019) with black dots with errorbars, and the relation obtained by McConnell & Ma (2013) with a green and shaded area.