  We show that, in the Thomas-Fermi regime, the cores of vortices in rotating
dilute Bose-Einstein condensates adjust in radius as the rotation velocity,
$\Omega$, grows, thus precluding a phase transition associated with core
overlap at high vortex density. In both a harmonic trap and a rotating
hard-walled bucket, the core size approaches a limiting fraction of the
intervortex spacing. At large rotation speeds, a system confined in a bucket
develops, within Thomas-Fermi, a hole along the rotation axis, and eventually
makes a transition to a giant vortex state with all the vorticity contained in
the hole.
