Abstract: The possibility of application of nanomaterials is determined by our ability to control the properties of the materials, which are ultimately determined by their structure and hence their growth processes. We employ hybrid molecular dynamics / Monte Carlo (MD/MC) simulations to explore the growth of SWNTs and graphene on nickel as a catalyst, with the specific goal of unraveling the growth mechanisms. While the general observations are in agreement with the literature, we find a number of interesting phenomena to be operative which are crucial for the growth, and which are not accessible by MD simulations alone due to the associated time scale. Specifically, we observe metal mediated healing and restructuring processes to take place, reorganizing the carbon network during the initial nucleation step. In the case of carbon nanotube growth, this leads to the growth of tubes with a determinable chirality. In the case of graphene formation, we find that graphene is only formed at temperatures above 700 K. These results are of importance for understanding the growth mechanisms of these carbon nanomaterials on the fundamental level.