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Broad Absorption Line (BAL) QSOs have been suggested to be youthfulsuper-accretors based on their powerful radiatively driven absorbing outflowsand often reddened continua. To test this hypothesis, we observed near IRspectra of the H$\beta$ region for 11 bright BAL QSOs at redshift z ~ 2. Wemeasured these and literature spectra for 6 BAL QSOs, 13 radio-loud and 7radio-quiet non-BAL QSOs. Using the luminosity and H$\beta$ broad line width toderive black hole mass and accretion rate, we find that both BAL and non-BALQSOs at z ~ 2 tend to have higher $L/L_{Edd}$ than those at low z -- probably aresult of selecting the brightest QSOs. However, we find that the high z QSOs,in particular the BAL QSOs, have extremely strong Fe II and very weak [O III],extending the inverse relationship found for low z QSOs. This suggests that,even while radiating near $L_{Edd}$, the BAL QSOs have a more plentiful fuelsupply than non-BAL QSOs. Comparison with low z QSOs shows for the first timethat the inverse Fe II -- [O III] relationship is indeed related to$L/L_{Edd}$, rather than black hole mass.Comment: 18 pages including 5 figures and 1 table. Accepted by the  Astrophysical Journal Letter

Eddington Accretion and QSO Emission Lines at z ~2