  We discuss the feasibility of quantum Hall states of vortices in trapped
low-density two-dimensional Bose gases with large particle interactions. For
interaction strengths larger than a critical dimensionless 2D coupling constant
$g_c \approx 0.6$, upon increasing the rotation frequency, the system is shown
to spatially separate into vortex lattice and melted vortex lattice (vortex
liquid) phases. At a first critical frequency, the lattice melts completely,
and strongly correlated vortex and particle quantum Hall liquids coexist in
inner respectively outer regions of the gas cloud. Finally, at a second
critical frequency, the vortex liquid disappears and the strongly correlated
particle quantum Hall state fills the whole sample.
