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Results of a statistical analysis of solar granulation are presented. A dataset of 36 images of a quiet Sun area on the solar disk center was used. Thedata were obtained with the 1.6 m clear aperture New Solar Telescope (NST) atBig Bear Solar Observatory (BBSO) and with a broad-band filter centered at theTiO (705.7 nm) spectral line. The very high spatial resolution of the data(diffraction limit of 77 km and pixel scale of 0.$"$0375) augmented by the veryhigh image contrast (15.5$\pm$0.6%) allowed us to detect for the first time adistinct subpopulation of mini-granular structures. These structures aredominant on spatial scales below 600 km. Their size is distributed as a powerlaw with an index of -1.8 (which is close to the Kolmogorov's -5/3 law) and nopredominant scale. The regular granules display a Gaussian (normal) sizedistribution with a mean diameter of 1050 km. Mini-granular structurescontribute significantly to the total granular area. They are predominantlyconfined to the wide dark lanes between regular granules and often form chainsand clusters, but different from magnetic bright points. A multi-fractalitytest reveals that the structures smaller than 600 km represent a multi-fractal,whereas on larger scales the granulation pattern shows no multi-fractality andcan be considered as a Gaussian random field. The origin, properties and roleof the newly discovered population of mini-granular structures in the solarmagneto-convection are yet to be explored.

Detection of Small-Scale Granular Structures in the Quiet Sun with the New Solar Telescope