We present new near infrared spectroscopic measurements for 29 luminous high-z quasars and use the data to discuss the size and other properties of the NLRs in those sources. The high resolution spectra have been used to carefully model the Fe II blends and to provide reliable [O III], Fe II and Hb measurements. We find that about 2/3 of all high luminosity sources show strong [O III] lines while the remaining objects show no or very weak such line. While weak [O III] emitters are also found among lower luminosity AGN, we argue that the implications for very high luminosity objects are different. In particular, we suggest that the averaging of these two populations in other works gave rise to claims of a Baldwin relationship in [O III] which is not confirmed by our data. We also argue that earlier proposed relations of the type R_NLR propto L_[O III]^{1/2}, where R_NLR is the NLR radius, are theoretically sound yet they must break down for R_NLR exceeding a few kpc. This suggests that the NLR properties in luminous sources are different from those observed in nearby AGN. In particular, we suggest that some sources lost their very large, dynamically unbound NLR while others are in a phase of violent star-forming events that produce a large quantity of high density gas in the central kpc. This gas is ionized and excited by the central radiation source and its spectroscopic properties may be different from those observed in nearby, lower luminosity NLRs. We also discuss the dependence of EW(Hb) and Fe II/Hb on L, M_BH, and accretion rate for a large sample of AGNs. The strongest dependence of the two quantities is on the accretion rate and the Fe II/Hb correlation is probably due to the EW(Hb) dependence on accretion rate. We show the most extreme values measured so far of Fe II/Hb and address its correlation with EW([O III]).
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