The origin of galaxy morphology has to be seen in the context of the hierarchical build up of structure and baryons expected in a CDM Universe. Star formation and structural properties of galaxies are well known to relate to their environment and stellar mass. We quantify the relation between galaxy morphology and both stellar and halo mass. In this talk, we present our sample, and the remarkably different morphological trends for the most massive ("central") and other ("satellite") galaxies in groups. We then interpret these trends both empirically and in the context of purpose-built recipes applied to two independent semi-analytic galaxies of galaxy formation, which account for the full merger history of galaxies.