  We generalize universal relations between the multifractal exponent \alpha_0
for the scaling of the typical wave function magnitude at a (Anderson)
localization-delocalization transition in two dimensions and the corresponding
critical finite size scaling (FSS) amplitude \Lambda_c of the typical
localization length in quasi-one-dimensional (Q1D) geometry: (i) When open
boundary conditions are imposed in the transverse direction of Q1D samples
(strip geometry), we show that the corresponding critical FSS amplitude
\Lambda_c^o is universally related to the boundary multifractal exponent
\alpha_0^s for the typical wave function amplitude along a straight boundary
(surface). (ii) We further propose a generalization of these universal
relations to those symmetry classes whose density of states vanishes at the
transition. (iii) We verify our generalized relations [Eqs. (6) and (7)]
numerically for the following four types of two-dimensional Anderson
transitions: (a) the metal-to-(ordinary insulator) transition in the spin-orbit
(symplectic) symmetry class, (b) the metal-to-(Z_2 topological insulator)
transition which is also in the spin-orbit (symplectic) class, (c) the integer
quantum Hall plateau transition, and (d) the spin quantum Hall plateau
transition.
