third model (C) removes the requirement of a sharp cutoff at the Eddington limit and instead adopts a steep power-law distribution with a tail to very high Eddington ratios, while retaining the 0.38 dex scatter in the [${\mathcal{M}_\mathrm{bh}}$]{}–[${\mathcal{M}_*}$]{} scaling. The Eddington limit only strictly applies to a spherical geometry and studies of accretion disk physics do allow for scenarios when the Eddington limit is violated [e.g. @Jaroszynski80; @Abramowicz88; @Begelman06]. Indeed, SMBHs accreting above their Eddington limits are rare but are found in sufficiently large samples of AGNs [e.g. @Mclure04; @Kelly13]. The slope of this high accretion rate tail has not been directly measured in our observed specific accretion rate distribution [although hints of such a turnover may be seen by @Bongiorno12]. We therefore introduce this as a single free parameter, $\gamma_2$, in our model that we fit using the original binned data points in our observed XLF (shown in Figure \[fig:xlf\]). We constrain the slope to be $\gamma_2=-2.1^{+0.3}_{-0.5}$. [[ We note that while the Eddington limit does provide a physically motivated scaling for our distributions, a turn over at precisely this point may not be realistic. If we allow the break in the distribution to be an additional free parameter 