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The radiative efficiencies ($\eta$) of 72 luminous unobscured Active GalacticNuclei (AGNs) at $z\sim1.5-3.5$, powered by some of the most massive blackholes (BHs), are constrained. The analysis is based on accretion disk (AD)models, which link the continuum luminosity at rest-frame optical wavelengthsand the black hole mass ($M_{\rm BH}$) to the accretion rate through the AD,$\dot{M}_{\rm AD}$. The data are gathered from several literature samples withdetailed measurements of the ${\rm H}\beta$ emission line complex, observed atnear-IR bands. When coupled with standard estimates of bolometric luminosities($L_{\rm bol}$), the analysis suggests high radiative efficiencies, with mostof the sources showing $\eta>0.2$ - that is, higher than the commonly assumedvalue of 0.1, and the expected value for non-spinning BHs ($\eta=0.057$). Evenunder more conservative assumptions regarding $L_{\rm bol}$ (i.e., $L_{\rmbol}=3\times \lambda L_{\lambda}$[5100$\AA$]), most of the extremely massiveBHs in the sample (i.e., $M_{\rm BH} > 3\times10^9\,M_{\rm \odot}$) showradiative efficiencies which correspond to very high BH spins ($a_{\rm *}$),with typical values well above $a_{\rm *}\simeq0.7$. These results stand incontrast to the predictions of a "spin-down"scenario, in which a series ofrandomly-oriented accretion episodes lead to $a_{\rm *}\simeq0$. Instead, theanalysis presented here strongly supports a "spin-up" scenario, which is drivenby either prolonged accretion or a series of anisotropically-oriented accretionepisodes. Considering the fact that these extreme BHs require long-durationcontinuous accretion to account for their high masses, it is argued that themost probable scenario for the SMBHs under study is that of an almostcontinuous sequence of randomly- yet not isotropically-oriented accretionepisodes.

The Most Massive Active Black-Holes at z~1.5-3.5 Have High Spins and Radiative Efficiencies