Based on our sample of 10 095 galaxies with bulge–disc decompositions we derive the empiricalBMGC‐band internal attenuation–inclination relation for galaxy discs and their associated central bulges. Our results agree well with the independently derived dust models of Tuffs et al., leading to a direct constraint on the mean opacity of spiral discs of τfB= 3.8 ± 0.7 (central face‐on BMGC‐band opacity). Depending on inclination, the BMGC‐band attenuation correction varies from 0.2 to 1.1 mag for discs and from 0.8 to 2.6 mag for bulges. We find that, overall, 37 per cent of all BMGC‐band photons produced in discs in the nearby Universe are absorbed by dust, a figure that rises to 71 per cent for bulge photons. The severity of internal dust extinction is such that one must incorporate internal dust corrections in all optical studies of large galaxy samples. This is particularly pertinent for optical Hubble Space Telescope comparative evolutionary studies as the dust properties will also be evolving. We use the new results to revise our recent estimates of the spheroid and disc luminosity functions. The implied stellar mass densities at redshift zero are somewhat higher than our earlier estimates: ρdiscs= (3.8 ± 0.6) → (4.4 ± 0.6) × 108 h M⊙ Mpc−3 and ρbulges= (1.6 ± 0.4) → (2.2 ± 0.4) × 108 h M⊙ Mpc−3. From our best‐fitting dust models we derive a redshift zero cosmic dust density of ρdust≈ (5.3 ± 1.7) × 105 h M⊙ Mpc−3. This implies that (0.0083 ± 0.0027)h per cent of the baryons in the Universe are in the form of dust and (11.9 ± 1.7) h per cent (Salpeter‐‘lite’ initial mass function) are in the form of stars (∼58 per cent reside in galaxy discs, ∼10 per cent in red elliptical galaxies, ∼29 per cent in classical galaxy bulges and the remainder in low‐luminosity blue spheroid systems/components).

We recover the joint and individual space density and surface‐brightness distribution(s) of galaxies from the Millennium Galaxy Catalogue (MGC). The MGC is a local survey spanning 30.9 deg2 and probing approximately 1–2 mag arcsec−2 deeper than either the Two‐Degree Field Galaxy Redshift Survey (2dFGRS) or the Sloan Digital Sky Survey (SDSS). The MGC contains 10 095 galaxies to BMGC < 20 mag with 96 per cent spectroscopic completeness. For each galaxy we derive individual K‐corrections and seeing‐corrected sizes. We implement a joint luminosity–surface‐brightness step‐wise maximum‐likelihood method to recover the bivariate brightness distribution (BBD) inclusive of most selection effects. Integrating the BBD over surface brightness we recover the following Schechter function parameters: φ*= (0.0177 ± 0.0015) h3 Mpc−3, M* italicB MGC− 5 log h= (−19.60 ± 0.04) mag and α=−1.13 ± 0.02. Compared to the 2dFGRS we find a consistent M* value but a slightly flatter faint‐end slope and a higher normalization, resulting in a final luminosity density j italicb J= (1.99 ± 0.17) × 108 h L⊙ Mpc−3– marginally higher than, but consistent with, the earlier 2dFGRS, ESP, and SDSS z= 0.1 results. The MGC is inconsistent with the SDSS z= 0.0 result (+3σ) if one adopts the derived SDSS evolution. The MGC surface‐brightness distribution is a well‐bounded Gaussian at the M* point with φ*= (3.5 ± 0.1) × 10−2h3 Mpc−3, μe*= (21.90 ± 0.01) mag arcsec−2 and σ ln italicR e= 0.35 ± 0.01. The characteristic surface brightness for luminous systems is invariant to M italicB MGC− 5 log h≈−19 mag faintwards of which it moves to lower surface brightness. The surface‐brightness distribution also broadens (σ ln italicR e≈ 0.5 − 0.7) towards lower luminosities. The luminosity dependence of σln Re provides a new constraint for both the theoretical development and numerical simulations, which typically predict a mass‐independent σ ln italicR e≈ 0.56 ± 0.04. Higher resolution (FWHM ≪ 1 arcsec) and deeper (μlim≫ 26 mag arcsec−2 in the B‐band) observations of the local Universe are now essential to probe to lower luminosity and lower surface‐brightness levels.

We have modelled the light distribution in 10 095 galaxies from the Millennium Galaxy Catalogue (MGC), providing publicly available structural catalogues for a large, representative sample of galaxies in the local Universe. Three different models were used: (1) a single Sérsic function for the whole galaxy, (2) a bulge–disc decomposition model using a de Vaucouleurs (R1/4) bulge plus exponential disc, (3) a bulge–disc decomposition model using a Sérsic (R1/n) bulge plus exponential disc. Repeat observations for ∼700 galaxies demonstrate that stable measurements can be obtained for object components with a half‐light radius comparable to, or larger than, the seeing half width at half‐maximum. We show that with careful quality control, robust measurements can be obtained for large samples such as the MGC. We use the catalogues to show that the galaxy colour bimodality is due to the two‐component nature of galaxies (i.e. bulges and discs) and not due to two distinct galaxy populations. We conclude that understanding galaxy evolution demands the routine bulge–disc decomposition of the giant galaxy population at all redshifts.