(ignoring major mergers) given it's observed redshift and stellar mass.
This letter by Alvio Renzini, discusses this issue. Renzini takes a recent parameterization of the SFR from the literature, and estimates how a galaxy at z=3 (when the universe was 2Gyr old) will grow. The upper red curve in the plot above shows the growth of stellar mass for the published parameterization... but obviously a typical observed galaxy can't grow in mass by 5 orders of magnitude from z=3 to z=0. So the lower red curves show how the growth will occur if you reduce the SFR at all redshifts by a factor of \eta.
The letter goes on to briefly discuss how environment, mergers, and morphological transformations/quenching will affect galaxy growth.