  We investigate the well-posedness and asymptotic self-similarity of solutions
to a generalized Smoluchowski coagulation equation recently introduced by
Bertoin and Le Gall in the context of continuous-state branching theory. In
particular, this equation governs the evolution of the L\'{e}vy measure of a
critical continuous-state branching process which becomes extinct (i.e., is
absorbed at zero) almost surely. We show that a nondegenerate scaling limit of
the L\'{e}vy measure (and the process) exists if and only if the branching
mechanism is regularly varying at 0. When the branching mechanism is regularly
varying, we characterize nondegenerate scaling limits of arbitrary
finite-measure solutions in terms of generalized Mittag-Leffler series.
