The molecular bases of periodontal tissue induction and regeneration are the osteogenic proteins of the transforming growth factor-β (TGF-β) supergene family. These morphogens act as soluble mediators for the induction of tissues morphogenesis sculpting the multicellular mineralized structures of the periodontal tissues with functionally oriented ligament fibers into newly formed cementum. Human TGF-β3 (hTGF-β3 ) in growth factor-reduced Matrigel® matrix induces cementogenesis when implanted in class II mandibular furcation defects surgically prepared in the non-human primate Chacma baboon, Papio ursinus. The newly formed periodontal ligament space is characterized by running fibers tightly attached to the cementoid surface penetrating as mineralized constructs within the newly formed cementum assembling and initiating within the mineralized dentine. Angiogenesis heralds the newly formed periodontal ligament space, and newly sprouting capillaries are lined by cellular elements with condensed chromatin interpreted as angioblasts responsible for the rapid and sustained induction of angiogenesis. The inductive activity of hTGF-β3 in Matrigel® matrix is enhanced by the addition of autogenous morcellated fragments of the rectus abdominis muscle potentially providing myoblastic, pericytic/perivascular stem cells for continuous tissue induction and morphogenesis. The striated rectus abdominis muscle is endowed with stem cell niches in para/perivascular location, which can be dominant, thus imposing stem cell features or stemness to the surrounding cells. This capacity to impose stemness is morphologically shown by greater alveolar bone induction and cementogenesis when hTGF-β3 in Matrigel® matrix is combined with morcellated fragments of autogenous rectus abdominis muscle. The induction of periodontal tissue morphogenesis develops as a mosaic structure in which the osteogenic proteins of the TGF-β supergene family singly, synergistically and synchronously initiate and maintain tissue induction and morphogenesis. In primates, the presence of several homologous yet molecularly different isoforms with osteogenic activity highlights the biological significance of this apparent redundancy and indicates multiple interactions during embryonic development and bone regeneration in postnatal life. Molecular redundancy with associated different biological functionalities in primate tissues may simply represent the fine-tuning of speciation-related molecular evolution in anthropoid apes at the early Pliocene boundary, which resulted in finer tuning of the bone induction cascade.