  We present the results of numerical calculations of the groundstates of
weakly-interacting Bose-Einstein condensates containing large numbers of
vortices. Our calculations show that these groundstates appear to be close to
uniform triangular vortex lattices. However, slight deviations from a uniform
triangular lattice have dramatic consequences on the overall particle
distribution. In particular, we demonstrate that the overall particle
distribution averaged on a lengthscale large compared to the vortex lattice
constant is well approximated by a Thomas-Fermi profile.
