  The critical two-terminal conductance $g_c$ and the spatial fluctuations of
critical eigenstates are investigated for a disordered two dimensional model of
non-interacting electrons subject to spin-orbit scattering (Ando model). For
square samples, we verify numerically the relation $\sigma_c=1/[2\pi(2-D(1))]
e^2/h$ between critical conductivity $\sigma_c=g_c=(1.42\pm 0.005) e^2/h$ and
the fractal information dimension of the electron wave function, $D(1)=1.889\pm
0.001$. Through a detailed numerical scaling analysis of the two-terminal
conductance we also estimate the critical exponent $\nu=2.80\pm 0.04$ that
governs the quantum phase transition.
