The RNA World theory for the origin of life requires polymers to be generated initially by abiotic reactions. Experiments have studied polymerization of 5′-monophosphates, 2′,3′-cyclic phosphates, and 5′-triphosphates. We consider theoretical models of polymerization in solution illustrating the differences between these cases. We consider (i) a basic model where all monomers undergo reversible joining and breaking; (ii) a model where 2′,3′-cyclic phosphates can join, and breaking regenerates the cyclic phosphate; (iii) a model where 5′-triphosphates can join irreversibly, in addition to the joining and breaking of 2′,3′-cyclic phosphates. In cases (i) and (ii) there is an equilibrium steady state with balance between making and breaking bonds. In case (iii) there is a circular reaction flux in which monomers are activated by an external phosphate source, activated monomers form polymers, and polymers break to release non-activated monomers. The mean length can be calculated as a function of concentration. In case (iii), the mean length switches from a low-concentration regime controlled by the 5′-triphosphates to a high-concentration regime controlled by the 2′,3′-cyclic phosphates. The circular reaction flux is reminiscent of a metabolism. If formation of 5’-triphosphates was already in place for RNA synthesis, ATP could subsequently been co-opted for metabolism.