Abstract The initiation of superfluorescence from N ≦ 70 atoms distributed randomly over the volume of a sphere is investigated by numerical computations. When a specified atomic configuration is changed by performing similarity transformations the cooperation number approaches an asymptotic value ≫ 1 for mean distances ≲ λ/50. This number does not depend on inhomogeneous broadening but sensitively depends on the specified random distribution of atoms. The mean value of the asymptotic cooperation number calculated for many configurations is near to √N.