The counter cation influence (H+, Na+, K+ and Li+) on the aggregates formation in aqueous solution of the salts of cobaltabisdicarbollide [1]- and its derivatives (monoiodinated [I-1]- and diiodinated [I2-1]-) has been studied by means of 11B{1H} and 1H{11B} NMR spectroscopy. 11B{1H} NMR spectrum of M[1] (M= alkali or H+) in water exhibits much wider signals than in an organic solvent because organic solvents (acetone) cause disaggregation. The wider resonances are found at concentrations larger than 10 mM while the sharpest signals are found below 10 mM, in which a large fraction of H[1] is in monomeric form and only a small fraction of H[1] participate in the formation of vesicles that has been visualized by CryoTEM. 11B{1H} NMR of H[1] at concentrations lower than 10 mM corresponds to the monomer and the phase transition that is observed is due to the monomer to micelles transformation. The 11B-NMR is, therefore, an excellent probe to visualize the phase transition between vesicles/monomer and micelles/monomer that appears between 10 and 20mM, for all tested cations. The 1H{11B} NMR spectra contribute interesting complementary information to the one retrieved from the 11B{1H} NMR, particularly in what concerns to dihydrogen bonds formation, C-H···H-B. These results have been compared with available crystal structures, which reveal the presence of such intermolecular dihydrogen bonds as responsible of the aggregates formation of [1]- in water. Computational analysis of the intermolecular interactions and self-assembly of the anions [1]- [I2-1]- are presented.