We present new H and K bands spectroscopy of 15 high luminosity active galactic nuclei (AGNs) at redshifts 2.3-3.4 obtained on Gemini South. We combined the data with spectra of additional 29 high-luminosity sources to obtain a sample with 10^{45.2}<lambda L_{lambda}(5100A)<10^{47.3} ergs/sec and black hole (BH) mass range, using reverberation mapping relationships based on the H_beta method, of 10^{8.8}-10^{10.7} M_sun. We do not find a correlation of L/L_Edd with M_BH but find a correlation with lambda L_{lambda}(5100A) which might be due to selection effects. The L/L_Edd distribution is broad and covers the range ~0.07-1.6, similar to what is observed in lower redshift, lower luminosity AGNs. We suggest that this consistently measured and calibrated sample gives the best representation of L/L_Edd at those redshifts and note potential discrepancies with recent theoretical and observational studies. The lower accretion rates are not in accord with growth scenarios for BHs at such redshifts and the growth times of many of the sources are longer than the age of the universe at the corresponding epochs. This suggests earlier episodes of faster growth at z>~3 for those sources. The use of the C IV method gives considerably different results and a larger scatter; this method seems to be a poor M_BH and L/L_Edd estimator at very high luminosity.
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