We study the self-assembly of peptide amphiphile (PA) molecules, which is governed by hydrophobic interactions between alkyl tails and a network of hydrogen bonds between peptide blocks. We demonstrate that the interplay between these two interactions results in the formation of assemblies of different morphology, in particular, single P-sheets connected laterally by hydrogen bonds, stacks of parallel P-sheets, spherical micelles, micelles with P-sheets in the corona, and long cylindrical fibers. We characterize the size distribution of the aggregates as a function of the molecular interactions. Our results suggest that the fort-nation of nanofibers of peptide amphiphiles obeys an open association model, which resembles living polymerization.