  We extend the results of a previous paper on the Gross-Pitaevskii description
of rotating Bose-Einstein condensates in two-dimensional traps to confining
potentials of the form V(r) = r^s, $2<s <\infty$. Writing the coupling constant
as $1/\epsilon^2$ we study the limit $\epsilon \to 0$. We derive rigorously the
leading asymptotics of the ground state energy and the density profile when the
rotation velocity \Omega tends to infinity as a power of $1/\epsilon$. The case
of asymptotically homogeneous potentials is also discussed.
