  Randomly branching polymers with {\em annealed} connectivity are model
systems for ring polymers and chromosomes. In this context, the branched
structure represents transient folding induced by topological constraints. Here
we present computer simulations of melts of annealed randomly branching
polymers of $3 \le N \le 1800$ segments in $d=2$ and $d=3$ dimensions. In all
cases, we perform a detailed analysis of the observed tree connectivities and
spatial conformations. Our results are in excellent agreement with an
asymptotic scaling of the average tree size of $R \sim N^{1/d}$, suggesting
that the trees behave as compact, {\it territorial} fractals. The observed
swelling relative to the size of ideal trees, $R\sim N^{1/4}$, demonstrates
that excluded volume interactions are only partially screened in melts of
annealed trees. Overall, our results are in good qualitative agreement with the
predictions of Flory theory. In particular, we find that the trees swell by the
combination of modified branching and path stretching. However, the former
effect is subdominant and difficult to detect in $d=3$ dimensions.
