as luminous galaxies are merged out of existence.

In the present paper, we explore this issue in light of the non-parametric model for the mass luminosity relation presented in @paper2 (hereafter paper I; see also @paper1). The basic idea behind the non-parametric model is to adopt the simple proposition that more luminous galaxies are hosted in more massive haloes/subhaloes. No attempt at physical modelling is made and the association is made simply by matching one-to-one the rank ordered observational list of galaxies with the rank ordered computed list of haloes/subhaloes. We here extend this model by introducing scatter into it, and also by considering possible effects on the total disruption of some subhaloes into the total luminosity related to the halo.

As is the case in HOD models (e.g., @bg [@zehavi; @zz]), this model naturally gives rise to a separation between central and satellite galaxies, by associating the former with the parent halo itself and the latter with the subhaloes associated with it. We analyze this issue in more detail, studying how it affects the cluster galaxy luminosity function and gives rise to a bright end bump caused by the central galaxies. We then develop a model for the BCG 