Context. The most highly accreting quasars are of special interest in studies of the physics of active galactic nuclei (AGNs) and host galaxy evolution. Quasars accreting at high rates (L/L_Edd ∼ 1) hold promise for use as “standard candles”: distance indicators detectable at very high redshift. However, their observational properties are still largely unknown.Aims. We seek to identify a significant number of extreme accretors. A large sample can clarify the main properties of quasars radiating nearL/L_Edd ∼ 1 (in this paper they are designated as extreme Population A quasars or simply as extreme accretors) in theHβspectral range for redshift ≲0.8.Methods. We use selection criteria derived from four-dimensional Eigenvector 1 (4DE1) studies to identify and analyze spectra for a sample of 334 candidate sources identified from the SDSS DR7 database. The source spectra were chosen to show a ratioR_FeIIbetween the FeII emission blend atλ4570 andHβ,R_FeII> 1. Composite spectra were analyzed for systematic trends as a function of Fe IIstrength, line width, and[OIII]strength. We introduced tighter constraints on the signal-to-noise ratio (S/N) andR_FeIIvalues that allowed us to isolate sources most likely to be extreme accretors.Results. We provide a database of detailed measurements. Analysis of the data allows us to confirm thatHβshows a Lorentzian function with a full width at half maximum (FWHM) ofHβ≤ 4000 km s⁻¹. We find no evidence for a discontinuity at 2000 km s⁻¹in the 4DE1, which could mean that the sources below this FWHM value do not belong to a different AGN class. Systematic[OIII]blue shifts, as well as a blueshifted component inHβare revealed. We interpret the blueshifts as related to the signature of outflowing gas from the quasar central engine. The FWHM ofHβis still affected by the blueshifted emission; however, the effect is non-negligible if the FWHMHβis used as a “virial broadening estimator” (VBE). We emphasize a strong effect of the viewing angle onHβbroadening, deriving a correction for those sources that shows major disagreement between virial and concordance cosmology luminosity values.Conclusions. The relatively large scatter between concordance cosmology and virial luminosity estimates can be reduced (by an order of magnitude) if a correction for orientation effects is included in the FWHMHβvalue; outflow and sample definition yield relatively minor effects.