  Recently, Lanzetta et al. (2002) have measured the distribution of star
formation rate intensity in galaxies at various redshifts. This data set has a
number of advantages relative to galaxy luminosity functions; the effect of
surface-brightness dimming on the selection function is simpler to understand,
and this data set also probes the size distribution of galactic disks. We
predict this function using semi-analytic models of hierarchical galaxy
formation in a LCDM cosmology. We show that the basic trends found in the data
follow naturally from the redshift evolution of dark matter halos. The data are
consistent with a constant efficiency of turning gas into stars in galaxies,
with a best-fit value of 2%, where dust obscuration is neglected; equivalently,
the data are consistent with a cosmic star formation rate which is constant to
within a factor of two at all redshifts above two. However, the practical
ability to use this kind of distribution to measure the total cosmic star
formation rate is limited by the predicted shape of an approximate power law
with a smoothly varying power, without a sharp break.
