Extensive full-atomistic molecular dynamics simulations are performed to study the self-organization of C60-fullerene dyad molecules in water, namely phenyl-C61-butyric acid methyl ester and fulleropyrrolidines, which have two elements of ordering, the hydrophobic fullerene cage and the hydrophilic/ionic group. While pristine fullerene or phenyl-C61-butyric acid methyl ester forms spherical droplets in order to minimize the surface tension, the amphiphilic nature of charged solute molecules leads to the formation of supramolecular assemblies having cylindrical shape driven by charge repulsion between the ionic groups located on the surface of the aggregates. We show that formation of non-spherical micelles is the geometrical consequence if the fullerene derivatives are considered as surfactants where the ionized groups are only hydrophilic unit. The agglomeration behavior of fullerenes is evaluated by determining sizes of the clusters, solvent accessible surface areas, and shape parameters. By changing the size of the counterions from chloride over iodide to perchlorate we find a thickening of the cylinder-like structures which can be explained by stronger condensation of larger ions and thus partial screening of the charge repulsion on the cluster surface. The reason for the size dependence of counterion condensation is the formation of a stronger hydration shell in case of small ions which in turn are repelled from the fullerene aggregates. Simulations are also in good agreement with the experimentally observed morphologies of decorated C60-nanoparticles.