  In this paper we develop a Bethe approximation, based on the cluster
variation method, which is apt to study lattice models of branched polymers. We
show that the method is extremely accurate in cases where exact results are
known as, for instance, in the enumeration of spanning trees. Moreover, the
expressions we obtain for the asymptotic number of spanning trees and lattice
trees on a graph coincide with analogous expressions derived through different
approaches. We study the phase diagram of lattice trees with nearest-neighbour
attraction and branching energies. We find a collapse transition at a
tricritical theta point, which separates an expanded phase from a compact
phase. We compare our results for the theta transition in two and three
dimensions with available numerical estimates.
