  In a recent paper (arXiv:0911.2514), one of us (FYW) considered the Potts
model and bond and site percolation on two general classes of two-dimensional
lattices, the triangular-type and kagome-type lattices, and obtained
closed-form expressions for the critical frontier with applications to various
lattice models. For the triangular-type lattices Wu's result is exact, and for
the kagome-type lattices Wu's expression is under a homogeneity assumption. The
purpose of the present paper is two-fold: First, an essential step in Wu's
analysis is the derivation of lattice-dependent constants $A, B, C$ for various
lattice models, a process which can be tedious. We present here a derivation of
these constants for subnet networks using a computer algorithm. Secondly, by
means of a finite-size scaling analysis based on numerical transfer matrix
calculations, we deduce critical properties and critical thresholds of various
models and assess the accuracy of the homogeneity assumption. Specifically, we
analyze the $q$-state Potts model and the bond percolation on the 3-12 and
kagome-type subnet lattices $(n\times n):(n\times n)$, $n\leq 4$, for which the
exact solution is not known. To calibrate the accuracy of the finite-size
procedure, we apply the same numerical analysis to models for which the exact
critical frontiers are known. The comparison of numerical and exact results
shows that our numerical determination of critical thresholds is accurate to 7
or 8 significant digits. This in turn infers that the homogeneity assumption
determines critical frontiers with an accuracy of 5 decimal places or higher.
Finally, we also obtained the exact percolation thresholds for site percolation
on kagome-type subnet lattices $(1\times 1):(n\times n)$ for $1\leq n \leq 6$.
