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tokens: H β +[OIII] lines after the subtraction of the continuum. The red curve represents the best-fit retrieval model from MC fits, and the shaded area encompass 68% of the MC sample; the black curve shows the [OIII] best fit obtained by Shen (2016) . Table B.1. [OIII] best-fit parameters. Notes. For each component, we report the amplitude (in erg s −1 cm −2 Å −1 ), the centroid, and the width of the best-fit Gaussian profile. B.1. Modelling rest-frame optical spectra The H α +[NII]+[SII] and H β +[OIII]+FeII systems of J0149+1501, J1421+2241, J1431+0535, J1436+6336, and J1220+0004 are redshifted in the K and H bands, respectively. We simultaneously fitted the continuum and all emission lines to reduce the degeneracies between BLR, NLR, and FeII emission. In short, we fitted a (single) power-law continuum, an optical FeII template ( Kovačević et al. 2010 ), and a combination of Gaussian functions to model BLR and NLR emission lines. In particular, depending on the complexity of FeII emission, we considered one or two FeII templates (see e.g. Vietri et al. 2018 ). These were convolved with a Gaussian; the width of this Gaussian, the amplitude normalisations, and velocity offset of the FeII templates were free variables in our fit (see Perna et al. 2017a for further details). Gaussian components were used to reproduce the emission lines. Specifically, we used (1) a systemic narrow ( F W H M 700 km s −1 ) Gaussian component for the [OIII] doublet and for the H β , H α , [NII], and [SII] doublets associated with unperturbed NLR emission; (2) a broad ( F W H M > 2000 km s −1 ) Gaussian component to fit the BLR H β and H α emission; and (3) an outflow ( F W H M > 700 km s −1 ) Gaussian component for all forbidden and permitted emission lines to reproduce prominent and asymmetric wings associated with outflowing gas. One or more additional sets of Gaussian components were considered to reproduce more complex profiles, for instance, asymmetric BLR emission lines (see e.g. J1421+2241, Fig. B.1 ) and extremely broad [OIII] profiles (e.g. J0843+0750, Fig. B.2 ; see also Fig. 11 in Coatman et al. 2019 ). Fig. B.2. Parametrisation of the MgII+FeII+FeIII ( left ) and H β +[OIII]+FeII ( middle and right panels ) of z > 2.5 QSO1 from the sample of Shen (2016) . The red lines show the best-fit from multiple systemic, outflow, and broad Gaussian profiles to the line features, together with a two local power laws to the continuum and one (two) template(s) to the FeII features (see text). Each curve with a different colour represent a distinct Gaussian set (or a FeII template) with same kinematic properties, as labeled in the figure. In the right panel we show, for each target, the spectrum around the H β +[OIII] lines after the subtraction of the continuum. The red curve represents the best-fit retrieval model from MC fits, and the shaded area encompass 68% of the MC sample; the black curve shows the [OIII] best-fit obtained by Shen (2016) . For J2238−0921, we do not