Tau-related dementias appear to involve specific to each disease aggregation pathways and morphologies of filamentous tau assemblies. To understand etiology of these differences, here we elucidate molecular mechanism of formation of tau PHFs based on the PMO theory of misfolding and aggregation of pleiomorphic proteins associated with neurodegenerative diseases. In this model, fibrillization of tau is initiated by the coupled binding and folding of the MTB domains that yields antiparallel homodimers, in analogy to folding of split inteins. The free energy of binding is minimized when the antiparallel alignment brings about backbone-backbone H-bonding between the MTBD segments of similar “strand” propensities. To assess these propensities, a function of the NMR shielding tensors of the Cα atoms is introduced as the folding potential function FPi; the Cα tensors are obtained by the quantum mechanical modeling of protein secondary structure (GIAO//B3LYP/D95**). The calculated FPi plots show that the “strand” propensities of the MBTD segments, and hence the homodimer's register, can be affected by the relatively small changes in the environment's pH, as a result of protonation of MBTD's conserved histidines. The assembly of the antiparallel tau dimers into granular aggregates and their subsequent conversion into the parallel cross-β structure of paired helical filaments is expected to follow the same path as the previously described fibrillization of Aβ. Consequently, the core structure of the nascent tau fibril is determined by the register of the tau homodimer. This model accounts for the reported differences in (i) fibril-core structure of in vivo and in vitro filaments, (ii) cross-seeding of isoforms, (iii) effects of reducing/non-reducing conditions, (iv) effects of PHF6 mutations, and (v) homologs' aggregation properties. The proposed model also suggests that in contrast to Alzheimer's and chronic traumatic encephalopathy disease, the assembly of tau prions in Pick's disease would be facilitated by a moderate drop in pH that accompanies e.g., transit in the endosomal system, inflammation response or an ischemic injury.