Correlation between BCG stellar mass and M₅₀₀ at z = 0. Observations are taken from DeMaio et al. (2018) (blacks quares) and Kravtsov et al. (2018) (black triangles). The simulated values are shown as blue points. The red hexagon refers to the BCG that lost its central BH (see Sect. 2.3.1). The orange line is the fit to LR simulations (Ragone-Figueroa et al. 2018). BCG masses are obtained summing over all stellar particles bound to the main subhalo of a group or cluster by Subfind (BCG+ICL) and within a 2D aperture of 50 pkpc.