We make use of multi-wavelength data of a large hyperluminous infrared (HLIRG) sample to derive their main physical properties, e.g., stellar mass, star-formation rate (SFR), volume density, contribution to the cosmic stellar mass density and to the cosmic SFR density. We also study the black hole (BH) growth rate and its relationship with the SFR of the host galaxy. We select 526 HLIRGs in three deep fields (Bo$o$tes, Lockman-Hole, ELAIS-N1) and adopt two spectral energy distribution (SED) fitting codes, CIGALE, which assumes energy balance, and CYGNUS, which is based on radiative transfer models and does not adopt energy balance principle. We use two different active galactic nucleus (AGN) models in CIGALE and three AGN models in CYGNUS to compare the results estimated using different SED fitting codes and different AGN models. The stellar mass, total IR luminosity and AGN luminosity agree well between different models with a typical median offset of 0.1 dex. The SFR estimates show the largest dispersions (up to 0.5 dex). This dispersion has an impact on the subsequent analysis, which may suggest that previous contradictory results could partly be due to different choices of methods. HLIRGs are ultra-massive galaxies with 99% of them having stellar masses larger than $10^{11} M_{odot}$. Our results reveal a higher space density of ultra-massive galaxies than found in previous surveys or predicted by simulations. We find that HLIRGs contribute more to the cosmic SFR density as redshift increases. In terms of BH growth, the two SED fitting methods provide different results. We can see a clear trend in which SFR decreases as AGN luminosity increases when using CYGNUS estimates, possibly implying quenching by AGN, while this trend is much weaker when using CIGALE estimates. This difference is also influenced by the dispersion between SlFR estimates obtained by the two codes.
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