  We study the critical behaviour of spherically symmetric scalar field
collapse to black holes in spacetime dimensions other than four. We obtain
reliable values for the scaling exponent in the supercritical region for
dimensions in the range $3.5\leq D\leq 14$. The critical exponent increases
monotonically to an asymptotic value at large $D$ of $\gamma\sim0.466$. The
data is well fit by a simple exponential of the form: $\gamma \sim
0.466(1-e^{-0.408 D})$.
