  We use a three-dimensional radiation transfer code to calculate the
steady-state escape fraction of ionizing photons from disk galaxies as a
function of redshift and galaxy mass. The gaseous disks are assumed to be
isothermal (with a sound speed $c_s\sim 10~{\rm km~s^{-1}}$) and radially
exponential. Their scale-radius is related to the characteristic spin parameter
and virial radius of their host halos, and their vertical structure is dictated
by their self-gravity. The sources of radiation are taken to be either stars
embedded in the disk, or a central quasar. The predicted increase in the disk
density with redshift results in an overall decline of the escape fraction with
increasing redshift. For typical parameters of smooth disks, we find that the
escape fraction at $z\sim 10$ is $\la 1%$ for stars, but $\ga 30%$ for
mini-quasars. Unless the smooth gas content of high-redshift disks was depleted
by more than an order of magnitude due to supernovae-driven outflows or
fragmentation, the reionization of the universe was most likely dominated by
mini-quasars rather than by stars.
