We have assembled a sample of five X-ray-absorbed and submm-luminous type 1 QSOs at z ∼ 2 which are simultaneously growing their central black holes through accretion and forming stars copiously. We present here the analysis of their rest-frame UV-to-submm spectral energy distributions (SEDs), including new Herschel data. Both AGN (direct and reprocessed) and star formation (SF) emission are needed to model their SEDs. From the SEDs and their UV–optical spectra we have estimated the masses of their black holes M BH ∼ 109–1010 M⊙, their intrinsic AGN bolometric luminosities L BOL ∼ (0.8–20) × 1013 L⊙, Eddington ratios L BOL/L Edd ∼ 0.1–1.1 and bolometric corrections $L_{\rm BOL}/L_{\rm X,2{\rm -}10}\sim 30{-}500$ . These values are common among optically and X-ray-selected type 1 QSOs (except for RX J1249), except for the bolometric corrections, which are higher. These objects show very high far-infrared luminosities L FIR ∼ (2–8) × 1012 M⊙ and star formation rates SFR ∼1000 M⊙ yr−1. From their L FIR and the shape of their FIR–submm emission we have estimated star-forming dust masses of M DUST ∼ 109 M⊙. We have found evidence of a tentative correlation between the gas column densities of the ionized absorbers detected in X-ray ( $N_{\rm H_{ion}}$ ) and SFR. Our computed black hole masses are amongst the most massive known.