by taking the asymptotic limit $K_f=0$. If $k_f^+=0$ this will be true for any value of $k_f^- \neq 0$. Within this approximation we can compare the effect of *end evaporation and addition* and *body evaporation and addition* explicitly. In this limit the equilibrium polymerised monomeric mass for a nucleus size of $n_c=2$ becomes \[eq8\] M() = -. In the absence of *body evaporation and addition*, i.e., for $\kpb=\kmb=0$, the polymerised monomeric mass becomes $M(\infty)=\mtot-\kme/\kpe=\mtot-K_e^{-1}$, where $K_e \equiv \kpe/\kme$. In the absence of *body evaporation and addition*, the ratio of rate constants $K_e$ can be mapped onto the equilibrium constant used in the thermodynamic theory of linear self-assembly. [@paul_review] In that case, in the polymerised regime, $y_1(\infty)= K_e^{-1}$, remains equal to the critical concentration. Hence, in this limit the polymerised monomeric mass is in agreement with the thermodynamic theory of self-assembly. [@paul_review] However, in the presence of *body evaporation and addition* pathway the effective elongation constant has to be renormalized to account for the free energy associated with monomer addition to or removal from the ends and that associated with monomer addition or removal along the backbone of the polymer.

In the limit $K_f \rightarrow 0$ the steady-state number of polymers 