Dehydropolymerisation of methylamine borane (H₃B⋅NMeH₂) using the well‐known iron amido complex [(PNP)Fe(H)(CO)] (PNP=N(CH₂CH₂PiPr₂)₂) (1) gives poly(aminoborane)s by a chain‐growth mechanism. In toluene, rapid dehydrogenation of H₃B⋅NMeH₂ following first‐order behaviour as a limiting case of a more general underlying Michaelis–Menten kinetics is observed, forming aminoborane H₂B=NMeH, which selectively couples to give high‐molecular‐weight poly(aminoborane)s (H₂BNMeH)_n and only traces of borazine (HBNMe)₃ by depolymerisation after full conversion. Based on a series of comparative experiments using structurally related Fe catalysts and dimethylamine borane (H₃B⋅NMe₂H) polymer formation is proposed to occur by nucleophilic chain growth as reported earlier computationally and experimentally. A silyl functionalised primary borane H₃B⋅N(CH₂SiMe₃)H₂ was studied in homo‐ and co‐dehydropolymerisation reactions to give the first examples for Si containing poly(aminoborane)s.