  We study the ground states of a 2D focusing non-linear Schr\"odinger equation
with rotation and harmonic trapping. When the strength of the interaction
approaches a critical value from below, the system collapses to a profile
obtained from the optimizer of a Gagliardo--Nirenberg interpolation inequality.
This was established before in the case of fixed rotation frequency. We extend
the result to rotation frequencies approaching, or even equal to, the critical
frequency at which the centrifugal force compensates the trap. We prove that
the blow-up scenario is to leading order unaffected by such a strong
deconfinement mechanism. In particular the blow-up profile remains independent
of the rotation frequency.
