  We present an updated determination of nuclear parton distributions (nPDFs)
from a global NLO QCD analysis of hard processes in fixed-target lepton-nucleus
and proton-nucleus together with collider proton-nucleus experiments. In
addition to neutral- and charged-current deep-inelastic and Drell-Yan
measurements on nuclear targets, we consider the information provided by the
production of electroweak gauge bosons, isolated photons, jet pairs, and
charmed mesons in proton-lead collisions at the LHC across centre-of-mass
energies of 5.02 TeV (Run I) and 8.16 TeV (Run II). For the first time in a
global nPDF analysis, the constraints from these various processes are
accounted for both in the nuclear PDFs and in the free-proton PDF baseline. The
extensive dataset underlying the nNNPDF3.0 determination, combined with its
model-independent parametrisation, reveals strong evidence for nuclear-induced
modifications of the partonic structure of heavy nuclei, specifically for the
small-$x$ shadowing of gluons and sea quarks, as well as the large-$x$
anti-shadowing of gluons. As a representative phenomenological application, we
provide predictions for ultra-high-energy neutrino-nucleon cross-sections,
relevant for data interpretation at neutrino observatories. Our results provide
key input for ongoing and future experimental programs, from that of heavy-ion
collisions in controlled collider environments to the study of high-energy
astrophysical processes.
