  We describe the density profiles of confined atomic Bose gases in the
high-rotation limit, in single-layer and multi-layer geometries. We show that,
in a local density approximation, the density in a single layer shows a
landscape of quantized steps due to the formation of incompressible liquids,
which are analogous to fractional quantum Hall liquids for a two-dimensional
electron gas in a strong magnetic field. In a multi-layered set-up we find
different phases, depending on the strength of the inter-layer tunneling t. We
discuss the situation where a vortex lattice in the three-dimensional
condensate (at large tunneling) undergoes quantum melting at a critical
tunneling $t_{c_1}$. For tunneling well below $t_{c_1}$ one expects weakly
coupled or isolated layers, each exhibiting a landscape of quantum Hall
liquids. After expansion, this gives a radial density distribution with
characteristic features (cusps) that provide experimental signatures of the
quantum Hall liquids.
