fainter galaxies in the cluster, or on the contrary, they are merely the extreme values of the same global distribution derived for all cluster galaxies.

On the theoretical side, there has been renewed interest in this subject with recent studies of the relation between galaxies and their dark matter haloes from a theoretical, statistical point of view, involving the study of the distribution of the galaxy population through different haloes while bypassing the complications of the physics of galaxy formation (e.g., @bg [@paper1; @iro; @yanghod; @zehavi; @zz; @coorayc; @charlie; @vdb]). Since these involve populating dark matter haloes with galaxies, they usually lead to a distinction between central and satellite galaxies. This in turn has lead to, in many of these works, central galaxies being treated separately from the rest, and therefore having a distinct distribution, with consequences visible, for example, in the luminosity function. Some of these studies have in fact looked at some specific BCG-related properties of clusters, like the magnitude gap (e.g., @milos [@vdb]).

In the past, observational studies which have focused on this issue [@tr; @hgt; @sgh; @bb84; @hs; @bhavsar; @pl; @bb] have been hindered by the limited numbers of high luminosity galaxy observations available, since the 