We investigate the dynamics of and the relations between small-scale penumbral and photospheric features near the outer penumbral boundary: penumbral grains (PGs), dark penumbral fibrils, granules, and photospheric G-band bright points. The analysis is based on a 2 h time sequence of a sunspot close to disc center, taken simultaneously in the G-band and in the blue continuum at 450.7 nm. Observations were performed at the Swedish Vacuum Solar Telescope (La Palma) in July 1999. A total of 2564 images (46 arcsec × 75 arcsec) were corrected for telescope aberrations and turbulence perturbations by applying the inversion method of phase diversity. Our findings can by summarized as follows: (a) one third of the outward-moving PGs pass through the outer penumbral boundary and then either continue moving as small bright features or expand and develop into granules. (b) Former PGs and G-band bright points next to the spot reveal a different nature. The latter have not been identified as a continuation of PGs escaping from the penumbra. The G-band bright points are mostly born close to dark penumbral fibrils where the magnetic field is strong, whereas PGs stem from the less-magnetized penumbral component and evolve presumably to non-magnetic granules or small bright features.