We study, via Brownian dynamics simulation, the kinetics of formation of branched loop-less structures for a mixture of particles with functionalities of two and three, the three-functional ones providing the branching points in the resulting network. We show that for this system, by combining the appropriate Smoluchowski rate equations, including condensation and fragmentation terms, with the thermodynamic perturbation theory of Wertheim, it is possible to provide a parameter-free description of the assembly process, even in the limit of irreversible aggregation (low T). Our work provides evidence of a connection between physical and chemical gelation in low-valence particle systems, properly relating aging (or curing) time with temperature. © The Royal Society of Chemistry.