Histograms of magnitudes and stellarity of objects with anomalous astrometric offsets in DES (top row), and in SkyMapper with Dec < −70 (bottom row). Different nested histograms correspond to incremental cuts in hybrid colours and limiting magnitude, and to a strict extragalactic cut in WISE. The limiting i-band magnitude is chosen as i_lim = 21 for DES, corresponding to current limits for spectroscopic follow-up on ≈4 m class telescopes, and i_lim = 19 for SkyMapper, simply as the limiting depth of its DR1. WISE preselection is not a limiting factor for wide and shallow searches (i ≲ 19), but it does become the main limitation in deeper searches (i ≲ 21).