Distribution of the properties of the max sub-sample sources (filled in regions) in comparison to the full sample of this study (main histogram). From top to bottom we compare: the bolometric luminosity of the quasars (L_bol), the IR (8–1000 μm) luminosity of the galaxies (L_IR), the S_peak, the FWHM, and the rms of the of the individual [C II] lines (before the velocity rebinning). It is evident that the max sub-sample covers a wide range of values in all properties, and is not skewed towards the brightest quasars, specific line-widths or line strength. The max sub-sample does seem to prefer higher rms values, but this is restricted by small number statistics.