[Abridged] In this paper we derive the central stellar mass density within a fixed radius and the effective stellar mass density within the effective radius for a complete sample of 34 ETGs morphologically selected at 0.92. Also, we show that the small scatter of the central mass density of ETGs compared to the large scatter of the effective mass density is simply a peculiar feature of the Sersic profile hence, independent of redshift and of any assembly history experienced by galaxies. Thus, it has no connection with the possible inside-out growth of ETGs. Finally, we find a tight correlation between the central stellar mass density and the total stellar mass of ETGs in the sense that the central mass density increases with mass as M^{~0.6}. This implies that the fraction of the central stellar mass of ETGs decreases with the mass of the galaxy. These correlations are valid for the whole population of ETGs considered independently of their redshift suggesting that they originate in the early-phases of their formation.
