The empirical model of Lu et al. is updated with recent data of galaxy stellar mass functions (SMFs). The model predicts that the slope of galaxy SMFs at z > 2 should be quite steep at the low-mass end, beyond the current detection limit, and it is a strong prediction that can be tested against future observations. The model is used to investigate the galaxy star formation and assembly or merger histories in detail. Most of the stars in cluster centrals, corresponding to brightest cluster galaxies in observations, formed earlier than z ≈ 2 but have been assembled much later. Typically, they have experienced ≈5 major mergers since their star formation was quenched. Milky Way mass galaxies have had on-going star formation without significant mergers since z ≈ 2, and are thus free of significant (classic) bulges produced by major mergers. Dwarf galaxies in haloes with Mh < 1011 h−1 M⊙ or M⋆ < 109 M⊙ have experienced a star formation burst at z > 2, followed by a nearly constant star formation rate after z = 1, and the stellar age decreases with stellar mass, contrary to the ‘downsizing’ trend for more massive galaxies. Major mergers are not uncommon during the early burst phase and may result in the formation of old spheroids in dwarf galaxies. We also characterize the stellar population of halo stars in different haloes.