A simple and efficient numerical model describing the processes of nucleation, growth, and transport of multicomponent nanoparticles is developed. The approach is similar to the classical method of moments but can be applied to co-condensation of several substances. The processes of homogeneous nucleation, heterogeneous growth, and coagulations due to Brownian collisions are considered in combination with the convective and diffusive transport of particles and reacting gases within multidimensional geometries. The model is applied to the analysis of multi-component co-condensation of TaC nanoparticles within a DC plasma reactor.