between host mass and galaxy luminosity can then be built through this process, with results that match well with observations (see paper I for a detailed analysis). The resulting relation can be well fit by a double power law of the type:

$$\label{mlfit}
L_{ref}(M)=L_0\frac{(M/M_0)^a}{[1+(M/M_0)^{b k}]^{1/k}} \, ,$$

where the differents parameters are shown in table \[mlfitparam\]; mass is in units of $h^{-1} {\rm M}_\odot$, luminosity in $h^{-2} {\rm L}_\odot$. The fit was done in the mass range $10^{11}$ ($3\times 10^{10}$ in the $b_j$ band case) to $3\times10^{15}$ $h^{-1} {\rm M}_\odot$.

\[mlfitparam\]

                 K-band               $b_J$-band
  ------- --------------------- ----------------------
  $L_0$    $1.37\times10^{10}$    $4.12\times 10^9$
  $M_0$     $6.14\times10^9$     $1.66\times 10^{10}$
  $a$             21.03                 6.653
  $b$             20.74                 6.373
  $k$            0.0363                 0.111

  : Fit parameters for the mass-luminosity relation.

![Mass-luminosity relation as obtained using the non-parametric model, in the K- and $b_J-$ bands. Upper pannel shows galaxy luminosity normalized to the characteristic luminosity, $L^*$, of each band; lower pannel shows the corresponding mass-to-light ratio.[]{data-label="mlfig"}](fig1a.ps "fig:"){width="84mm"} ![Mass-luminosity relation as obtained using the non-parametric model, in the K- and $b_J-$ bands. Upper pannel shows galaxy luminosity normalized to the characteristic luminosity, $L^*$, of each band; lower pannel shows the corresponding mass-to-light ratio.[]{data-label="mlfig"}](fig1b.ps "fig:"){width="84mm"}

Figure \[mlfig\] shows the results for the luminosity 