tokens: with redshift in terms of the density parameters of both SF and AGN components of the RLF. In terms of luminosity evolution, parameters of both the SF and AGN components are consistent with being constant with redshift. We note that the normalization of the radio luminosity function of optically selected quasars by Kimball et al. (2011) and Condon et al. (2013) , shown in the first panel of Fig. 6 , is more than an order of magnitude lower than that constrained by fitting our data with the analytic RLF form of Eq. ( 8 ). The main cause of this difference is most likely different sample selection. While optically-selected quasar samples by Kimball et al. and Condon et al. contain only the unobscured quasars, sampling quasars with very high bolometric luminosities, our XQSO sample contains a combination of both obscured and unobscured quasars. By examining the hardness ratios (HRs) of XQSOs ( Civano et al. 2016 , Marchesi et al. 2016 , Pierre et al. 2016 ) and applying a threshold of HR = −0.2 to separate obscured from unobscured sources (e.g., Civano et al. 2012 ), we found that most of XQSOs (190/274) are obscured based on their X-ray emission and most likely would not be included in samples of optically-selected quasars. 5. Discussion In this section, we discuss the possible contributions to the detected radio emission: star-forming processes within the host galaxy in Sect. 5.1 and AGN activity in Sect. 5.2 . In Sect. 5.3 we define thresholds in 1.4 GHz radio luminosity below and above which more than 80% of the XQSOs are dominated by the star formation and AGN-related radio emission, respectively. This enables us to disclose the true composite nature of the XQSOs in which both star formation and AGN activity make a significant contribution to the radio luminosity. 5.1. Host galaxies of XQSOs The sample of XQSOs studied in this work was drawn from the moderate-to-high radiative luminosity AGN sample in COSMOS and high-excitation radio galaxy sample of AGN in XXL-S. Host galaxy properties of these AGN have been studied by Delvecchio et al. (2017 ; COSMOS) and in Paper XXXI (XXL-S). Both studies found that the host galaxies of these AGN have star formation rates (SFRs) and stellar masses consistent with typical main-sequence galaxies. The same conclusion was reached by Stanley et al. (2015) from an analysis of a sample of ∼2000 X-ray selected AGN (10 42 erg s −1 L 2−8 keV 10 45.5 erg s −1 ) detected in the Chandra Deep Field North and South and the COSMOS field. They studied the distribution of star formation-related IR luminosity and X-ray luminosity over 0.2 z 2.5, as proxies of SFRs and AGN activity, respectively. They found a strong evolution of their average L IR, SF with redshift, similar to that observed for the main-sequence galaxies. These results were confirmed by multiple other studies of quasar and AGN host galaxy properties (e.g., Rosario et al. 2012 , 2013 , Lanzuisi et al. 2017 , Stanley et al. 2017 , Suh et al. 2017 , 2019 ).
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