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We present a "super-deblended" far-infrared to (sub)millimeter photometriccatalog in the Cosmic Evolution Survey (COSMOS), prepared with the methodrecently developed by Liu et al. 2018, with key adaptations. We obtain pointspread function (PSF) fitting photometry at fixed prior positions including88,008 galaxies detected in either VLA 1.4~GHz, 3~GHz and/or MIPS 24~$\mu$mimages. By adding a specifically carved mass-selected sample (with an evolvingstellar mass limit), a highly complete prior sample of 194,428 galaxies isachieved for deblending FIR/(sub)mm images. We performed ``active' removal ofnon relevant priors at FIR/(sub)mm bands using spectral energy distribution(SED) fitting and redshift information. In order to cope with the shallowerCOSMOS data we subtract from the maps the flux of faint non-fitted priors andexplicitly account for the uncertainty of this step. The resulting photometry(including data from Spitzer, Herschel, SCUBA2, AzTEC, MAMBO and NSF's Karl G.Jansky Very Large Array at 3~GHz and 1.4~GHz) displays well behavedquasi-Gaussian uncertainties, calibrated from Monte Carlo simulations andtailored to observables (crowding, residual maps). Comparison to ALMAphotometry for hundreds of sources provide a remarkable validation of thetechnique. We detect 11,220 galaxies over the 100--1200~$\mu$m range, extendingto $z_{\rm phot}\sim7$. We conservatively selected a sample of 85 $z>4$ highredshift candidates, significantly detected in the FIR/(sub)mm, often withsecure radio and/or Spitzer/IRAC counterparts. This provides a chance toinvestigate the first generation of vigorous starburst galaxies(SFRs$\sim1000\mathrm{M}_\odot$~yr$^{-1}$). The photometric and value addedcatalogs are publicly released.

"Super-deblended" Dust Emission in Galaxies: II. Far-IR to (sub)millimeter photometry and high redshift galaxy candidates in the full COSMOS field