We have constructed an extended halo model (EHM) which relates the total stellar mass and star-formation rate (SFR) to halo mass (M h). An empirical relation between the distribution functions of total stellar mass of galaxies and host halo mass, tuned to match the spatial density of galaxies over 0 < z < 2 and the clustering properties at z ∼ 0, is extended to include two different scenarios describing the variation of SFR on M h. We also present new measurements of the redshift evolution of the average SFR for star-forming galaxies of different stellar masses up to z = 2, using data from the Herschel Multi-tiered Extragalactic Survey for infrared bright galaxies. Combining the EHM with the halo accretion histories from numerical simulations, we trace the stellar mass growth and star-formation history in haloes spanning a range of masses. We find that: (1) the intensity of the star-forming activity in haloes in the probed mass range has steadily decreased from z ∼ 2 to 0; (2) at a given epoch, haloes in the mass range between a few times 1011 M and a few times 1012 M are the most efficient at hosting star formation; (3) the peak of SFR density shifts to lower mass haloes over time; and (4) galaxies that are forming stars most actively at z ∼ 2 evolve into quiescent galaxies in today's group environments, strongly supporting previous claims that the most powerful starbursts at z ∼ 2 are progenitors of today's elliptical galaxies.