What is the evolutionary mechanism for the TCR‐MHC‐conserved interaction? We extend Dembic's model (Dembic Z. In, Scand J Immunol e12806, 2019) of thymus positive selection for high‐avidity anti–self‐MHC Tregs among double (CD4 + CD8+)‐positive (DP) developing thymocytes. This model is based on competition for self‐MHC (+ Pep) complexes presented on cortical epithelium. Such T cells exit as CD4 + CD25+FoxP3 + thymic‐derived Tregs (tTregs). The other positively selected DP T cells are then negatively selected on medulla epithelium removing high‐avidity anti–self‐MHC + Pep as T cells commit to CD4 + or CD8 + lineages. The process is likened to the competitive selection and affinity maturation in Germinal Centre for the somatic hypermutation (SHM) of rearranged immunoglobulin (Ig) variable region (V[D]Js) of centrocytes bearing antigen‐specific B cell receptors (BCR). We now argue that the same direct SHM processes for TCRs occur in post‐antigenic Germinal Centres, but now occurring in peripheral pTregs. This model provides a potential solution to a long‐standing problem previously recognized by Cohn and others (Cohn M, Anderson CC, Dembic Z. In, Scand J Immunol e12790, 2019) of how co‐evolution occurs of species‐specific MHC alleles with the repertoire of their germline TCR V counterparts. We suggest this is not by ‘blind’, slow, and random Darwinian natural selection events, but a rapid structured somatic selection vertical transmission process. The pTregs bearing somatic TCR V mutant genes then, on arrival in reproductive tissues, can donate their TCR V sequences via soma‐to‐germline feedback as discussed in this journal earlier. (Steele EJ, Lindley RA. In, Scand J Immunol e12670, 2018) The high‐avidity tTregs also participate in the same process to maintain a biased, high‐avidity anti–self‐MHC germline V repertoire.