[en] Using the cosmological baryonic accretion rate and normal star formation (SF) efficiencies, we present a very simple model for star-forming galaxies that accounts for the mass and redshift dependences of the star formation rate (SFR)-mass and Tully-Fisher (TF) relations from z ∼ 2 to the present. The time evolution follows from the fact that each modeled galaxy approaches a steady state where the SFR follows the (net) cold gas accretion rate. The key feature of the model is a halo mass floor M _min ≅ 10¹¹ M_sun below which accretion is quenched in order to simultaneously account for the observed slopes of the SFR-mass and TF relations. The same successes cannot be achieved via an SF threshold (or delay) nor by varying the SF efficiency or the feedback efficiency. Combined with the mass ceiling for cold accretion due to virial shock heating, the mass floor M_min explains galaxy 'downsizing', where more massive galaxies formed earlier and over a shorter period of time. It turns out that the model also accounts for the observed galactic baryon and gas fractions as a function of mass and time, and the cosmic SFR density, which are all resulting from the mass floor M _min. The model helps us to understand that it is the cosmological decline of accretion rate that drives the decrease of cosmic SFR density between z ∼ 2 and z = 0 and the rise of the cosmic SFR density from z ∼ 6 to z ∼ 2 that allows us to put a constraint on our main parameter M _min ≅ 10¹¹ M_sun. Among the physical mechanisms that could be responsible for the mass floor, our view is that photoionization feedback (from first in situ hot stars) lowering the cooling efficiency is likely to play a large role.