2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138025Building on and from the work of Brydges and Imbrie, we give an elementary calculation of the volume of the space of branched polymers of order $n$ in the plane and in 3-space. Our development reveals some more general identities, and allows exact random sampling. In particular we show that a random 3-dimensional branched polymer of order $n$ has diameter of order $\sqrt{n}$.20 pages, 11 figuresProbabilityMathematical Physics82D60; 82B21text