In the present work, we investigate the capacity of the niobium atom adsorbed on the carbon and boron nitride planar flakes to store hydrogen molecules. Specifically, the Nb adsorbed on the circumcoronene (Nb@C), hexagonal boron nitride (Nb@h − BN), and the h − BN with the central ring substituted by carbons (Nb@C6/h − BN). The Nb@C and Nb@C6/h − BN systems present a hybridization among the carbon and niobium orbitals, which implies higher binding energy between the Nb atom and the corresponding flake, contrasting with the observed for the Nb@h − BN cluster. All the Nb@flakes possess multiplicity different from one, reinforcing the importance of considering the various accessible spin-state. Despite the high number of adsorbed hydrogen molecules supported by the Nb@flakes, the stability of the whole system is affected as the number of molecular hydrogen increases. The Nb@C6/h − BN is the system that satisfies the conditions of stability and H2 storage capacity. We highlight that the storage capacity of a given system must be measured considering not only the number of hydrogen molecules supported by the structure but also taking into account how the presence of nH2 affects the stability of the whole material.