[en] The precipitation of niobium carbides in industrial steels is commonly used to control the recrystallization process or the amount of interstitial atoms in solid solution. It is then important to understand the precipitation kinetics and especially the competition between homogeneous and heterogeneous precipitation, since both of them have been observed experimentally, depending on they alloy composition, microstructure and thermal treatments. We propose Monte Carlo simulations of NbC precipitation in □-iron, based on a simple atomic description of the main parameters which control the kinetic pathway: - Realistic diffusion properties, with a rapid diffusion of C atoms by interstitial jumps and a slower diffusion of Fe and Nb atoms by vacancy jumps; - A model of grain boundaries which reproduces the segregation properties of Nb and C; - A model of dislocation which interacts with solute atoms through local segregation energies and long range elastic field; - A point defect source which drives the vacancy concentration towards its equilibrium value. Depending on the precipitation conditions, Monte Carlo simulations predict different kinetic behaviors, including a transient precipitation of metastable carbides, an early segregation stage of C, wetting phenomena at grain boundaries and on dislocations and a competition between homogeneous and heterogeneous NbC precipitation. Concerning the last point, we highlight that long range elastic field due to dislocation favors clearly the heterogeneous precipitation on dislocations. To understand this effect, we have developed a heterogeneous nucleation model including the calculation of the local concentration of solute atoms around the dislocation, the change of the solubility limit relative to the solubility limit in bulk and the energy of precipitates in an elastic field. We have concluded that elastic field favors the heterogeneous precipitation through the fall in nucleation barrier. (author)