  The expansion factor, $\alpha^{2}=\langle s_{N}^{2}\rangle/\langle
s_{N}^{2}\rangle_{0}$, of branched molecules in the melt state is estimated.
The equilibrium expansion factor is determined as the point in which all the
inhomogeneity terms of the osmotic potential, $\Delta G_{osmotic}$, go to zero.
Numerical analysis shows that $\log\,\alpha=0.082\,\log N+\text{const.}$ for
$10^{3}\le N\le 10^{7}$, giving $\alpha\cong \text{const.}\,N^{1/12}$ so that
$\langle s_{N}^{2}\rangle^{1/2}\propto N^{1/3}$ which coincides with the value
for the critical packing density.
