Context : We present near-IR spectroscopy of a sample of luminous ( { M _ { B } < -27.5 } ; { L _ { bol } > 10 ^ { 14 } } ~ { } L _ { \odot } ) , sub-millimeter-detected , dusty ( { M _ { d } } \sim 10 ^ { 9 } ~ { } M _ { \odot } ) , radio-quiet quasi-stellar objects ( QSOs ) at z \sim 2 . Aims : A primary aim is to provide a more accurate QSO redshift determination in order to trace kinematics and inflows/outflows in these sub-mm bright QSOs . Additionally , the H \alpha and continuum properties allow an estimation of the black hole mass and accretion rate , offering insights into the starburst-AGN connection in sub-mm bright QSOs . Methods : We measure the redshift , width , and luminosity of the H \alpha line , and the continuum luminosity near H \alpha . Relative velocity differences between H \alpha and rest-frame UV emission lines are used to study the presence and strength of outflows/inflows . Luminosities and line widths are used to estimate the black hole masses , bolometric luminosities , Eddington fractions , and accretion rates ; these are compared to the star-formation-rate ( SFR ) , estimated from the sub-mm derived far-infrared ( FIR ) luminosity . Finally our sub-mm-bright QSO sample is compared with other QSO samples at similar redshifts . Results : The H \alpha emission line was strongly detected in all sources . Two components – a very broad ( \gtrsim 5000 km s ^ { -1 } ) Gaussian and an intermediate-width ( \gtrsim 1500 km s ^ { -1 } ) Gaussian , were required to fit the H \alpha profile of all observed QSOs . Narrow ( \lesssim 1000 km s ^ { -1 } ) lines were not detected in the sample QSOs . The rest-frame UV emission lines in these sub-mm bright QSOs show larger than average blue-shifted velocities , potentially tracing strong – up to 3000 km s ^ { -1 } – outflows in the Broad Line Region . With the exception of the one QSO which shows exceptionally broad H \alpha lines , the black hole masses of the QSO sample are in the range log M _ { BH } = 9.0–9.7 and the Eddington fractions are between 0.5 and \sim 1 . In black hole mass and accretion rate , this sub-mm bright QSO sample is indistinguishable from the Shemmer et al . ( 2004 ) optically-bright QSO sample at z \sim 2 ; the latter is likely dominated by sub-mm dim QSOs . Previous authors have demonstrated a correlation , over six orders of magnitude , between SFR and accretion rate in active galaxies : the sub-mm bright QSOs lie at the upper extremes of both quantities and their SFR is an order of magnitude higher than that predicted from the correlation . Conclusions :