  We present results from a detailed assessment of the ultimate constraining
power of LHC data on the PDFs that can be expected from the complete dataset,
in particular after the High-Luminosity (HL) phase. To achieve this, HL-LHC
pseudo-data for different projections of the experimental uncertainties are
generated, and the resulting constraints on the PDF4LHC15 set are quantified by
means of the Hessian profiling method. We find that HL-LHC measurements can
reduce PDF uncertainties by up to a factor of 2 to 4 in comparison to
state-of-the-art fits, leading to few-percent uncertainties for important
observables such as the Higgs boson transverse momentum distribution via
gluon-fusion. Our results illustrate the significant improvement in the
precision of PDF fits achievable from hadron collider data alone. In addition,
we apply the same methodology to the final anticipated data sample from the
proposed LHeC, and compare these with the HL-LHC projections, demonstrating an
encouraging complementarity between the projected HL-LHC and LHeC constraints.
