  The detection of the diffuse supernova neutrino background (DSNB) will
preciously contribute to gauge the properties of the core-collapse supernova
population. We estimate the DSNB event rate in the next-generation neutrino
detectors, Hyper-Kamiokande enriched with Gadolinium, JUNO, and DUNE. The
determination of the supernova unknowns through the DSNB will be heavily driven
by Hyper-Kamiokande, given its higher expected event rate, and complemented by
DUNE that will help in reducing the parameters uncertainties. Meanwhile, JUNO
will be sensitive to the DSNB signal over the largest energy range. A joint
statistical analysis of the expected rates in 20 years of data taking from the
above detectors suggests that we will be sensitive to the local supernova rate
at most at a 20-33% level. A non-zero fraction of supernovae forming black
holes will be confirmed at a 90% CL, if the true value of that fraction is
larger than 20%. On the other hand, the DSNB events show extremely poor
statistical sensitivity to the nuclear equation of state and mass accretion
rate of the progenitors forming black holes.
