Titanium dioxide nanotubes (TNT) have been extensively studied because of their unique properties, which make such systems ideal candidates for biomedical application, especially for the targeted release of drugs. However, knowledge about the properties of TiO2 nanotubes with typical dimensions of the order of the nanometer is limited, especially concerning the adsorption of molecules that can be potentially loaded in actual devices. In this work, we investigate, by means of simulations based on hybrid density functional theory, the adsorption of Vitamin C molecules on different nanotubes through a comparative analysis of the properties of different structures. We consider two different anatase TiO2 surfaces, the most stable (101) and the more reactive (001)A; we evaluate the role of the curvature, the thickness and of the diameter as well as of the rolling direction of the nanotube. Different orientations of the molecule with respect to the surface are studied in order to identify any trends in the adsorption mechanism. Our results show that there is no preferential functional group of the molecule interacting with the substrate, nor any definite spatial dependency, like a rolling orientation or the concavity of the nanotube. Instead, the adsorption is driven by geometrical factors only, i.e., the favorable matching of the position and the alignment of any functional groups with undercoordinated Ti atoms of the surface, through the interplay between chemical and hydrogen bonds. Differently from flat slabs, thicker nanotubes do not improve the stability of the adsorption, but rather develop weaker interactions, due to the enhanced curvature of the substrate layers.