We have updated our radially-resolved SAMs of galaxy formation, which track both the atomic and molecular gas phases of the ISM. The models are adapted from those of Guo et al. using similar methodology as in Fu et al. and are run on halo merger trees from the MS and MS II with the following main changes: (1) We adopt a simple star formation law where \Sigma_SFR \propto \Sigma_H2 (2) We inject the heavy elements produced by supernovae directly into the halo hot gas, instead of first mixing them with the cold gas in the disk. (3) We include radial gas inflows in disks using a model of the form v_inflow = \alpha r. The models are used to study the radial profiles of star formation rate and gas-phase metallicity in present-day galaxies. The \Sigma_H2 profiles in L* galaxies place strong constraints on inflow velocities, favouring models where v_inflow~7km/s at a galactocentric radius of 10kpc. Radial gas inflow has little influence on gas-phase and stellar metallicity gradients, which are affected much more strongly by the fraction of metals that are directly injected into the halo gas, rather than mixed with the cold gas. Metals ejected out of the galaxy in early epochs result in late infall of pre-enriched gas and flatter present-day gas-phase metallicity gradients. A prescription in which 80% of the metals are injected into the halo gas results in good fits to the flat observed metallicity gradients in galaxies with stellar masses greater than 10^10 M_sun, as well as the relations between gas-phase metallicity and sSFR in the outer parts of galactic disks. We examine the correlation between gas-phase metallicity gradient and global galaxy properties, finding that it is most strongly correlated with the bulge-to-total ratio of the galaxy. This is because gas is consumed when the bulge forms during galaxy mergers, and the gas-phase metallicity gradient is then set by newly-accreted gas.