In large spheroidal stellar systems , such as elliptical galaxies , one invariably finds a 10 ^ { 6 } - 10 ^ { 9 } M _ { \odot } supermassive black hole at their centre . In contrast , within dwarf elliptical galaxies one predominantly observes a 10 ^ { 5 } - 10 ^ { 7 } M _ { \odot } nuclear star cluster . To date , few galaxies have been found with both type of nuclei coexisting and even less have had the masses determined for both central components . Here we identify one dozen galaxies housing nuclear star clusters and supermassive black holes whose masses have been measured . This doubles the known number of such hermaphrodite nuclei — which are expected to be fruitful sources of gravitational radiation . Over the host spheroid ( stellar ) mass range 10 ^ { 8 } – 10 ^ { 11 } M _ { \odot } , we find that a galaxy ’ s nucleus-to-spheroid ( baryon ) mass ratio is not a constant value but decreases from a few percent to \sim 0.3 percent such that \log [ ( M _ { BH } + M _ { NC } ) / M _ { sph } ] = - ( 0.39 \pm 0.07 ) \log [ M _ { sph } / 10 ^ { % 10 } M _ { \odot } ] - ( 2.18 \pm 0.07 ) . Once dry merging has commenced by M _ { sph } \approx 10 ^ { 11 } M _ { \odot } and the nuclear star clusters have disappeared , this ratio is expected to become a constant value . As a byproduct of our investigation , we have found that the projected flux from resolved nuclear star clusters can be well approximated with Sérsic functions having a range of indices from \sim 0.5 to \sim 3 , the latter index describing the Milky Way ’ s nuclear star cluster .