Three examples of best-fit SEDs of HLAGN selected from different criteria. Coloured lines represent the corresponding best-fit templates of AGN (red), galaxy star formation (blue), and the sum of the two (black). Left panel: AGN identified from X-rays, MIR colours, and SED fitting. Central panel: AGN identified only from SED-fitting. Right panel: AGN identified only from X-rays. The red dashed line indicates that the AGN component is <99% significant on the basis of the Fisher test (see text for more details). Red circles indicate the optical to far-IR (FIR) photometry (rest-frame), while downward pointing arrows represent 3σ upper limits in the Herschel bands.