Recently, we disclosed the uncatalyzed formation of polyaminoboranes (PABs) from monomeric diisopropylaminoborane ((Pr2N)-Pr-i-BH2) and primary amines (RNH2). Their structure is studied through a detailed multinuclear NMR study and their full spectroscopic characterization is presented revealing that N-alkyl substituted PABs exhibit magnetically non-equivalent methylenic protons in the close vicinity of the BN-backbone. We also performed an in-depth theoretical study of this global chemical process. The mechanism is fully apprehended and the strong influence of the temperature on the outcome of the reaction is unveiled. DFT-calculations clearly show that the formation of the polyaminoboranes (RNH-BH2)(n) results from a kinetically controlled step-growth polymerization reaction that can be globally viewed as a head-to-tail association process of the in situ generated transient monomeric monoalkylamino-borane [RNH-BH2].