The relationship between Far-Infrared (FIR) luminosity and the mass accretion rate onto the black hole for sub-mm detected QSOs (filled circles with error bars). The equivalent axes of star formation rate (SFR) and bolometric luminosity are indicated on the right and top of the plot, respectively. The sub-mm QSOs are close to the highest end of the relationship between the two quantities found to be valid over 6 orders of magnitude (black line in the figure; Trakhtenbrot & Netzer 2010). QSOs at z  ~  2 observed in the mid-IR by Spitzer (Lutz et al. 2008) are plotted as squares; filled symbols are used for the QSOs in common with our sample.