The incorporation of impurities during the growth of nanowires from the vapour phase alters their basic properties substantially, and this process is critical in an extended range of emerging nanometre-scale technologies. In particular, achieving precise control of the behaviour of group III and group V dopants has been a crucial step in the development of silicon (Si) nanowire-based devices. Recently it has been demonstrated that the use of aluminium (Al) as a growth catalyst, instead of the usual gold, also yields an effective p-type doping, thereby enabling a novel and efficient route to functionalizing Si nanowires. Besides the technological implications, this self-doping implies the detachment of Al from the catalyst and its injection into the growing nanowire, involving atomic-scale processes that are crucial for the fundamental understanding of the catalytic assembly of nanowires. Here we present an atomic-level, quantitative study of this phenomenon of catalyst dissolution by three-dimensional atom-by-atom mapping of individual Al-catalysed Si nanowires using highly focused ultraviolet-laser-assisted atom-probe tomography. Although the observed incorporation of the catalyst atoms into nanowires exceeds by orders of magnitude the equilibrium solid solubility and solid-solution concentrations in known non-equilibrium processes, the Al impurities are found to be homogeneously distributed in the nanowire and do not form precipitates or clusters. As well as the anticipated effect on the electrical properties, this kinetics-driven colossal injection also has direct implications for nanowire morphology. We discuss the observed strong deviation from equilibrium using a model of solute trapping at step edges, and identify the key growth parameters behind this phenomenon on the basis of a kinetic model of step-flow growth of nanowires. The control of this phenomenon provides opportunities to create a new class of nanoscale devices by precisely tailoring the shape and composition of metal-catalysed nanowires.