  We present a minimal dynamical model for randomly branched isotropic
polymers, and we study this model in the framework of renormalized field
theory. For the swollen phase, we show that our model provides a route to
understand the well established dimensional-reduction results from a different
angle. For the collapse $\theta$-transition, we uncover a hidden
Becchi-Rouet-Stora super-symmetry, signaling the sole relevance of
tree-configurations. We correct the long-standing 1-loop results for the
critical exponents, and we push these results on to 2-loop order. For the
collapse $\theta^{\prime}$-transition, we find a runaway of the renormalization
group flow, which lends credence to the possibility that this transition is a
fluctuation-induced first-order transition. Our dynamical model allows us to
calculate for the first time the fractal dimension of the shortest path on
randomly branched polymers in the swollen phase as well as at the collapse
transition and related fractal dimensions.
