  We implement parallel versions of the GARM and Wang-Landau algorithms for
stars and for acyclic uniform branched networks in the square lattice. These
are models of monodispersed branched polymers, and we estimate the star vertex
exponents $\sigma_f$ for $f$-stars, and the entropic exponent
$\gamma_\mathcal{G}$ for networks with comb and brush connectivity in two
dimensions. Our results verify the predicted (but not rigorously proven) exact
values of the vertex exponents and we test the scaling relation [5] $$
\gamma_{\mathcal{G}}-1 = \sum_{f\geq 1} m_f \, \sigma_f $$ for the branched
networks in two dimensions.
