  We use the exceptional depth of the Ultra Deep Field (UDF) and UDF-Parallel
ACS fields to study the sizes of high redshift (z~2-6) galaxies and address
long-standing questions about possible biases in the cosmic star formation rate
due to surface brightness dimming. Contrasting B, V, and i-dropout samples
culled from the deeper data with those obtained from the shallower GOODS
fields, we demonstrate that the shallower data are essentially complete at
bright magnitudes to z<5.5 and that the principal effect of depth is to add
objects at the magnitude limit. This indicates that high redshift galaxies are
compact in size (~0.1-0.3") and that large (>0.4", >3 kpc) low surface
brightness galaxies are rare. A simple comparison of the half-light radii of
the HDF-N + HDF-S U-dropouts with B, V, and i-dropouts from the UDF shows that
the sizes follow a (1+z)^{-1.05+/-0.21} scaling towards high redshift. A more
rigorous measurement compares different scalings of our U-dropout sample with
the mean profiles for a set of intermediate magnitude (26.0<z_{850,AB}<27.5)
i-dropouts from the UDF. The best-fit is found with a (1+z)^{-0.94_{-0.25}
^{+0.19}} size scaling (for fixed luminosity). This result is then verified by
repeating this experiment with different size measures, low redshift samples,
and magnitude ranges. Very similar scalings are found for all comparisons. A
robust measurement of size evolution is thereby demonstrated for galaxies from
z~6 to z~2.5 using data from the UDF.
