Cumulative X-ray luminosity functions of ULX candidates from 4XMM, CSC2 and 2SXPS. Top panel: deconvolved XLF of spiral galaxies, and residuals from the single (middle) and broken (bottom) power-law fits detailed in Table 5. Bottom panel: deconvolved XLF of elliptical galaxies, and residuals from the single power-law fits detailed in Table 4. For comparison, we overlay the cumulative distributions of sources matching their host nucleus, and of ULX candidates classified as background contaminants.