Cobalt nanoparticles (NPs) synthesized in liquid environments present anisotropic shaped nanocrystals such as disks, plates, rods, wires or cubes. Though the synthesis parameters (precursor, reducing agent, stabilizing ligands, concentration, temperature or rate of precursor injection) controlling the final morphologies are experimentally well controlled, little is known concerning the growth mechanisms at the atomic scale. In this work, we intend to predict the morphology variation of hcp cobalt NPs as a function of the ligand concentration. To this aim, we consider two well-established thermodynamic models and develop a new kinetic one. These models require the knowledge of the adsorption behaviors of stabilizing molecules as a function of surface coverage on preferential facets of NPs. To this end, density functional theory (DFT) calculations were performed on the adsorption of a model carboxylate ligand CH₃COO on different Co crystalline surfaces. The shapes of the Co NPs obtained by these models are compared to experimental morphologies and other theoretical results from the literature. While thermodynamic models are in poor agreement with experimental observations, the variety of shapes predicted by the kinetic model is much more promising. Our study confirms that the morphological control of NPs is mostly driven by kinetic effects.