The relatively massive bulges and spheroids that we observe in the local Universe are predicted to originate from a sequence of galaxy-galaxy mergers. The number and type of galaxy mergers should therefore be correlated with the number and shape of bulges and spheroids. We, however, recently discovered a loophole in traditional models of galaxy formation: The number of galaxy mergers strongly depends on the underlying shape of the stellar mass-halo mass relation and thus ultimately on the galaxy stellar mass function. Thus, theoretical models that predict even moderate differences in galaxy numbers compared to observational measurements, can induce very discrepant numbers of galaxy mergers and hence of spheroids and bulges, rendering the comparison between models and data largely ineffective.  

In this talk I will present our newly-developed DREAM, a DiscREte stAtistical seMi-empirical model that, by simply relying on a single input, a data-driven SMHM relation, can predict many of the core properties of galaxies, namely galaxy star formation histories, merger histories, morphologies, and satellites abundances. In addition, DREAM is based on only a small set of assumptions, at variance with other more traditional approaches, and by design it mitigates computational limitations in volume and performance by weighting central and satellite galaxies via their number densities, avoiding object-by-object modelling. DREAM can however still generate full galaxy mocks at fixed redshift or along a light cone, thus representing an invaluable tool for the planning and testing of the imminent large galaxy missions Euclid and LSST.