A simple model is derived which, by including exit-channel effects into transition state theory (TST), allows a description of state distributions in the products of three-atom barrierless unimolecular reactions. Exit-channel effects, which reduce mainly to a transfer of energy between rotational and translational motions on the way from the transition state (TS) to the products, are described within the recently derived free-path integration model (FPIM). A transfer coefficient chi relating the magnitude of the transfer to the mechanical parameters of the system is evidenced. The model is applied to the reaction O2H-->O-2 + H in the case where it involves small transfers; semiquantitative agreement is found with quasiclassical trajectory (QCT) calculations. However, the model fails at describing product state distributions in the case of stronger transfers, demonstrating the necessity to go beyond FPIM.