Heterosupramolecular structures from CdSe or CdSe/ZnS core/shell nanocrystals and a specially designed organic fluorophore (diazaperylene) have been prepared to investigate the electronic interactions at nanoscopic semiconductor surfaces. To determine the average number of dye molecules per nanocrystal, we monitored the size-dependent molar extinction coefficient of CdSe particles. The NC/dye ratio is depending on the particle size and varies between 3 and 20 dye molecules per nanocrystal. We demonstrate that the fluorescence of the nanocrystals is completely quenched upon the formation of the supramolecular NC/dye complex even if the surface of the CdSe particles is covered with a few monolayers of the high band gap semiconductor ZnS.