  We study Anderson localization in two-dimensional systems with purely
off-diagonal disorder. Localization lengths are computed by the transfer-matrix
method and their finite-size and scaling properties are investigated. We find
various numerically challenging differences to the usual problems with diagonal
disorder. In particular, the divergence of the localization lengths close to
the band centre is investigated in detail for bipartite and non-bipartite
lattices as well as different distributions of the off-diagonal disorder.
Divergence exponents for the localization lengths are constructed that appear
to describe the data well down to at least 10^-5. We find only little evidence
for a crossover energy scale below which the power law has been argued to fail.
