luminosity distribution. Since the halo in fact arises from the union of subhaloes this non-parametric model is a statistically well defined variant of the cannibalism scenario.

This paper is organised as follows: in section 2, we give a brief summary of the non-parametric model relating galaxy luminosity with halo/subhalo mass presented in paper I, and introduce a simple recipe for checking the contribution of destroyed subhaloes to the halo mass, and how this changes our estimate of the total luminosity. In section 3, we introduce scatter into the non-parametric model by building a conditional luminosity function, where we consider two possibilities for it, either a simple lognormal shape or a better motivated approach involving the distribution of concentration for haloes of a given mass. In section 4, we explore more indepth how the model gives rise to a central/satellite galaxy separation, and show how this impacts the cluster galaxy luminosity function. In section 5, we build up a model for the distribution of cluster galaxies, based on the mass-luminosity relation and the halo/subhaloes separation which underpins it. In section 6, we present simple models to account for another two possible origins for the BCG distribution: first, we consider that all 