Growth on transition metal substrates is becoming a method of choice to prepare large-area graphene foils. In the case of nickel, where carbon has a significant solubility, such a growth process includes at least two elementary steps: (1) carbon dissolution into the metal, and (2) graphene precipitation at the surface. Here, we dissolve calibrated amounts of carbon in nickel films, using carbon ion implantation, and annealing at 725 circ or 900 circ. We then use transmission electron microscopy to analyse the precipitation process in detail: the latter appears to imply carbon diffusion over large distances and at least two distinct microscopic mechanisms.