  We outline the case for heavy-ion-physics studies using the multi-TeV lead
LHC beams in the fixed-target mode. After a brief contextual reminder, we
detail the possible contributions of AFTER@LHC to heavy-ion physics with a
specific emphasis on quarkonia. We then present performance simulations for a
selection of observables. These show that $\Upsilon(nS)$, $J/\psi$ and
$\psi(2S)$ production in heavy-ion collisions can be studied in new energy and
rapidity domains with the LHCb and ALICE detectors. We also discuss the
relevance to analyse the Drell-Yan pair production in asymmetric
nucleus-nucleus collisions to study the factorisation of the nuclear
modification of partonic densities and of further quarkonia to restore their
status of golden probes of the quark-gluon plasma formation.
