We report on the i-dropouts detected in two exceptionally deep Advanced Camera for Surveys fields (B435, V606, i775, and z850 with 10 σ limits of 28.8, 29.0, 28.5, and 27.8, respectively) taken in parallel with the Ultra Deep Field Near-Infrared Camera and Multi-Object Spectrometer observations. Using an i-z > 1.4 cut, we find 30 i-dropouts over 21 arcmin2 down to z850, AB = 28.1, or 1.4 i-dropouts arcmin-2, with significant field-to-field variation (as expected from cosmic variance). This extends i-dropout searches some ~0.9 mag further down the luminosity function than was possible in the Great Observatories Origins Deep Survey (GOODS) fields, yielding a ~7 times increase in surface density. An estimate of the size evolution for UV-bright objects is obtained by comparing the composite radial flux profile of the bright i-dropouts (z850, AB < 27.2) with scaled versions of the Hubble Deep Field-North and -South U-dropouts. The best fit is found with a (1 + z) scaling in size (for fixed luminosity), extending lower redshift (1 < z < 5) trends to z ~ 6. Adopting this scaling and the brighter i-dropouts from both GOODS fields, we make incompleteness estimates and construct a z ~ 6 luminosity function (LF) in the rest-frame continuum UV (~1350 A) over a 3.5 mag baseline, finding a shape consistent with that found at lower redshift. To evaluate the evolution in the LF from z ~ 3.8, we make comparisons against different scalings of a lower redshift B-dropout sample. Although a strong degeneracy is found between luminosity and density evolution, our best-fit model scales as (1 + z)-2.8 in number and (1 + z)0.1 in luminosity, suggesting a rest-frame continuum UV luminosity density at z ~ 6 that is just 0.38 times that at z ~ 3.8. Our inclusion of the size evolution makes the present estimate lower than previous z ~ 6 estimates.