For a two-dimensional lattice $Lambda$ with $n$ vertices, the number of spanning trees $N_{ST}(Lambda)$ grows asymptotically as $exp(n z_Lambda)$ in the thermodynamic limit. We present exact integral expression and numerical value for the asymptotic growth constant $z_Lambda$ for spanning trees on various two-dimensional lattices with more than one type of vertex given in cite{Okeeffe}. An exact closed-form expression for the asymptotic growth constant is derived for net 14, and the asymptotic growth constants of net 27 and the triangle lattice have the simple relation $z_{27} = (z_{tri}+ln 4)/4$. Some integral identities are also obtained.
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