The concerted action of a large number of individual molecular level events in the formation and growth of fibrillar protein structures creates a significant challenge for differentiating between the relative contributions of different self-assembly steps to the overall kinetics of this process. The characterization of the individual steps is, however, an important requirement for achieving a quantitative understanding of this general phenomenon which underlies many crucial functional and pathological pathways in living systems. In this study, we have applied a kinetic modeling approach to interpret experimental data obtained for the aggregation of a selection of site-directed mutants of the protein S6 from Thermus thermophilus. By studying a range of concentrations of both the seed structures, used to initiate the reaction, and of the soluble monomer, which is consumed during the growth reaction, we are able to separate unambiguously secondary pathways from primary nucleation and fibril elongation. In particular, our results show that the characteristic autocatalytic nature of the growth process originates from secondary processes rather than primary nucleation events, and enables us to derive a scaling law which relates the initial seed concentration to the onset of the growth phase.