We carry out numerical simulations of the collapse of a complex rotating
scalar field of the form $\Psi(t,r,\theta)=e^{im\theta}\Phi(t,r)$, giving rise
to anaxisymmetric metric, in 2+1 spacetime dimensions with $\Lambda<0$, for
$m=0,1,2$, for four 1-parameter families of initial data. We look for the
familiar scaling of black hole mass and maximal Ricci curvature as a power of
$|p-p_*|$, where $p$ is the amplitude of our initial data and $p_*$ some
threshold. We find evidence of Ricci scaling for all families, and tentative
evidence of mass scaling for most families, but the case $m>0$ is very
different from the case $m=0$ we have considered before: the thresholds for
mass scaling and Ricci scaling are significantly different (for the same
family), scaling stops well above the scale set by $\Lambda$, and the exponents
depend strongly on the family. Hence, in contrast to the $m=0$ case, and to
many other self-gravitating systems, there is only weak evidence for the
collapse threshold being controlled by a self-similar critical solution and no
evidence for it being universal.