Decoration of one-dimensional mull-walled carbon nanotubes (MWCNTs) with zero-dimensional Co nanoparticles leads to hybrid structures with chemical and electromagnetic features that are not available to the individual components. This work addresses the influence of the nature and structure of MWCNTs on the localization of Co nanoparticles. Depending on synthesis conditions, Co can be deposited on the external or in inner surfaces of the nanotubes. Co/MWCNTs hybrids have been characterized by in situ X-ray powder diffraction, high-resolution transmission electron microscopy and Co-59 internal field nuclear magnetic resonance. It has been shown that the average diameter (7.2, 9.4 and 18.6 nm), number of walls (5-7, 12-15, 15-20), and functional composition of the MWCNTs have a remarkable effect on the size of Co nanoparticles and their distribution in the structure of MWCNTs. The observed phenomenon has been rationalized in terms of nanotubes surface properties. Parent MWCNTs being hydrophobic and having limited porosity do not stabilize Co nanoparticles and, therefore, they are localized on the outside surface with relatively large average size and broad size distribution. On the other hand, the oxidation of the MWCNTs resulted in the penetration of Co nanoparticles inside of the nanotubes, presumably because of pore opening as well as increased hydrophilicity of the nanotubes.