  We use transfer-matrix and finite-size scaling methods to investigate the
location and properties of the multicritical point of two-dimensional Ising
spin glasses on square, triangular and honeycomb lattices, with both binary and
Gaussian disorder distributions. For square and triangular lattices with binary
disorder, the estimated position of the multicritical point is in numerical
agreement with recent conjectures regarding its exact location. For the
remaining four cases, our results indicate disagreement with the respective
versions of the conjecture, though by very small amounts, never exceeding 0.2%.
Our results for: (i) the correlation-length exponent $\nu$ governing the
ferro-paramagnetic transition; (ii) the critical domain-wall energy amplitude
$\eta$; (iii) the conformal anomaly $c$; (iv) the finite-size susceptibility
exponent $\gamma/\nu$; and (v) the set of multifractal exponents $\{\eta_k \}$
associated to the moments of the probability distribution of spin-spin
correlation functions at the multicritical point, are consistent with
universality as regards lattice structure and disorder distribution, and in
good agreement with existing estimates.
