We compute the baryonic mass function , \psi ^ { { } ^ { { } _ { S } } } ( M _ { b } ) d { log } M _ { b } , of disc galaxies using the luminosity functions and baryonic mass-to-light ratios reliable for this goal .
On scales from 10 ^ { 8 } M _ { \odot } to 10 ^ { 11 } M _ { \odot } this function is featureless , \psi ^ { { } ^ { { } _ { S } } } \propto M _ { b } ^ { -1 / 2 } .
Outside this mass range \psi ^ { { } ^ { { } _ { S } } } is a strong inverse function of M _ { b } .
The contributions to the baryon density \Omega ^ { { } ^ { { } _ { S } } } _ { b } from objects of different mass indicate that spirals have a characteristic mass scale at M _ { b } ^ { \oplus } \simeq 2 \times 10 ^ { 11 } M _ { \odot } , around which more than 50 % of the total baryonic mass is concentrated .
The integral value , \Omega _ { b } ^ { { } ^ { { } _ { S } } } = ( 1.4 \pm 0.2 ) \times 10 ^ { -3 } , confirms , to a higher accuracy , previous evidence ( Persic & Salucci 1992 ) that the fraction of BBN baryons locked in disc galaxies is negligible and matches that of high- z Damped Ly \alpha systems ( DLAs ) .
We investigate the scenario where DLAs are the progenitors of present-day spirals , and find a simple relationship between their masses and HI column densities by which the DLA mass function closely matches that of spiral discs .