  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 an axisymmetric metric, in 2+1 spacetime dimensions with cosmological
constant $\Lambda<0$, 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.
