Size-tuned hollow nanoparticles of MoS2 sulfides ("inorganic fullerenes", IF) have been prepared using topotactic solid-gas reaction of nanoparticulate scheelites AMoO(4) (A = Ca, Sr, Ba) with H2S/CCl4 mixtures in a wide range of temperatures. The hollow nanoparticles showed high specific surface areas and outstanding thermal stability. As shown by electron microscopy and Raman spectroscopy characterizations, the amounts of residual slabs edges and the curvature-related defects in the IF-MoS2 particles can be controlled independently by means of varying the particle size and the preparation temperature. The slabs edges disappear when the temperature increases, whereas the curvature - related defects withstand thermal treatments but their amount depends of the particle size. Temperature programmed reduction suggested the presence of sulfur species with a decreased bonding energy, attributed to the slabs curvature. Catalytic tests in the electrochemical hydrogen evolution reaction (HER) and thiophene hydrodesulfurization (HDS) evidenced significant contribution of curved basal planes to the catalytic activity, the magnitude of the effect being size-dependent.