We investigate the dust heating mechanisms of sub-mm galaxies (SMGs) to consider the contribution of Active Galactic Nuclei (AGN) compared to star-formation. We have used ALMA at $0.1$ resolution to image a complete sample of seven sub-mm sources previously shown to have spectral energy distributions (SEDs) that were as well-fitted by obscured AGN as star-forming galaxy templates. Indeed, two sub-mm sources were known to be quasars from their absorbed X-ray emission. We now find that the sub-mm sizes of all SMGs are small ($approx1-2$ kpc) and generally $>3times$ smaller than any host detected in the near-Infra-Red. In all cases, the five SMGs are comparable in sub-mm size to the two known quasars and four $zapprox6$ quasars, also observed with ALMA. We detect no evidence of diffuse spiral arms in this complete sample. We then convert the Far-Infra-Red (FIR) luminosities to star-formation rate (SFR) surface densities and find that the SMGs occupy the same range as the known quasars in our sample. We conclude that in terms of sub-mm size, extent relative to host and SFR density as well as luminosity and mid-IR colour, there is little distinction between the SMGs and sub-mm bright quasars. In light of these results, we continue to suggest that dust+gas absorbed quasars may simultaneously dominate the FIR and hard X-ray backgrounds.
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