  We study circularly-symmetric phase separation of vortex lattices in a
rapidly rotating harmonically-trapped quasi--two-dimensional binary
Bose-Einstein condensate (BEC) by introducing a weak quartic trap in one of the
components. The increase of the rotational frequency in such a system is also
found to generate a phase separation of the vortex lattices of an overlapping
non-rotating BEC. The phase-separated vortex lattices have different structures
for a binary BEC with inter-species repulsion and inter-species attraction. In
the former case of a fully repulsive binary BEC the phase separation of the
vortex-lattices is accompanied by a complete phase separation of component
densities. In the latter case of inter-species attraction there is a partial
phase separation of component densities, although there could be a complete
phase separation of the generated vortex lattices in the two components. In the
case of inter-species attraction, we need to have different intra-species
repulsion in the two components for an efficient phase separation. We compare
and contrast our results with the phase separation obtained in a
harmonically-trapped binary BEC without any quartic trap.
