Very Massive Galaxies: A Challenge for Hierarchical Models?

Hierarchical models of galaxy formation now provide a much closer match to observations than they did a few years ago. The progress has been achieved by adjusting the description of baryonic processes such as star formation and supernova/AGN feedback, while leaving the evolution of the underlying dark matter (DM) halos the same. Being most results very sensitive to the input baryonic physics, the ultimate vindication of the hierarchical paradigm should come from observational tests probing more directly the merging history of DM halos rather than the history of star formation. Two questions may start addressing this deeper level: is the predicted halo merging rate consistent with the observed galaxy merging rate? and, are predicted and observed evolution of the galaxy mass function consistent with each other. The current status of these issues is briefly reviewed.