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. to 10(11) M. this function is featureless, psi(S) proportional to M-b(-1/2). Outside this mass range psi(S) is a strong inverse function of Mb The contributions to the baryon density Omega(b)(S) from objects of different mass indicate that spirals have a characteristic mass scale at M-b(circle times) similar or equal to 2 X 10(11) M., around which more than 50 per cent of the total baryonic mass is concentrated. The integral value, Omega(b)(S) = (1.4 +/- 0.2) x 10(-3), confirms, to a higher accuracy, previous evidence 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.