  Branched polymers can be classified into two categories that obey the
different formulae: \begin{equation} \nu= \begin{cases}
\hspace{1mm}\displaystyle\frac{2(1+\nu_{0})}{d+2} & \hspace{3mm}\mbox{for
polymers
with}\hspace{2mm}\displaystyle\nu_{0}\ge\frac{1}{d+1}\hspace{10mm}\text{(I)}\\[3mm]
\hspace{5mm}2\nu_{0}& \hspace{3mm}\mbox{for polymers
with}\hspace{2mm}\displaystyle\nu_{0}\le\frac{1}{d+1}\hspace{10mm}\text{(II)}
\end{cases}\notag \end{equation} for the dilution limit in good solvents. The
category II covers the exceptional polymers having fully expanded
configurations. On the basis of these equalities, we discuss the size exponents
of the nested architectures and the lattice trees. In particular, we compare
our preceding result, $\nu_{d=2}=1/2$, for the $z$=2 polymer having
$\nu_{0}=1/4$ with the numerical result, $\nu_{d=2}\doteq 0.64115$, for the
lattice trees generated on the 2-dimensional lattice. Our conjecture is that
while both the conclusions in polymer physics and condensed matter physics are
correct, the discrepancy arises from the fact that the lattice trees are
constructed from less branched architectures than the branched polymers having
$\nu_{0} = 1/4$ in polymer physics. The present analysis suggests that the
2-dimensional lattice trees are the mixture of isomers having the mean ideal
size exponent of $\bar{\nu}_{0}\doteq0.32$.
