DOI: http://dx.doi.org/10.1007/s00601-012-0445-8

We outline the many quarkonium-physics opportunities offered by a multi-purpose fixed-target experiment using the p and Pb LHC beams extracted by a bent crystal. This provides an integrated luminosity of 0.5 fb-1 per year on a typical 1cm-long target. Such an extraction mode does not alter the performance of the collider experiments at the LHC. With such a high luminosity, one can analyse quarkonium production in great details in pp, pd and pA collisions at sqrt(sNN)~115 GeV and at sqrt(sNN)~72 GeV in PbA collisions. In a typical pp (pA) run, the obtained quarkonium yields per unit of rapidity are 2-3 orders of magnitude larger than those expected at RHIC and about respectively 10 (70) times larger than for ALICE. In PbA, they are comparable. By instrumenting the target-rapidity region, the large negative-xF domain can be accessed for the first time, greatly extending previous measurements by Hera-B and E866. Such analyses should help resolving the quarkonium-production controversies and clear the way for gluon PDF extraction via quarkonium studies. The nuclear target-species versatility provides a unique opportunity to study nuclear matter and the features of the hot and dense matter formed in PbA collisions. A polarised proton target allows the study of transverse-spin asymmetries in J/psi and Upsilon production, providing access to the gluon and charm Sivers functions Show Partial Abstract