Observed radio-excess 1.4 GHz luminosity function divided into four redshift bins (increasing from left to right). Data points (black circles) are binned with Δ(log L_1.4) = 0.4 dex. Correction for flux completeness is equally applied to all realisations, following previous VLA-COSMOS-based studies (e.g. Smolčić et al. 2017c; Novak et al. 2018; Ceraj et al. 2018). The best-fit PLE model from Smolčić et al. (2017c) is overlaid on each panel. This figure is split into four rows, as follows. (a): Dataset from Smolčić et al. (2017c, including SF and passive galaxies) obtained by applying the radio-excess criterion from Delvecchio et al. (2017). (b): Dataset from Smolčić et al. (2017c) but identifying radio-excess AGN according to D21. (c): Radio-excess AGN from this work (i.e. only within NUVrJ-based SFGs) identified based on Delvecchio et al. (2017). (d): This work following D21 (same as the pre-corrected RLF shown in Fig. B.1, top panel). The equivalent RLF by assuming a fixed spectral index (γ=–0.75) is shown for comparison (empty squares). See the text for details.