  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.
