Upper panel: normalised histograms of the high-z X-ray AGN selected through our analysis (red) and the DES sources inside the 4XMM-DES-VHS footprint (blue) as a function of the DES i-band magnitude. The vertical line indicates the mode of the DES i-band magnitude distribution for the latter at i_DES = 24.3 mag. Lower panel: fraction of high-z X-ray HSC sources that have a match with the DES DR2 catalogue.