  Heavy quarkonium production in ultra-peripheral nuclear collisions (UPC) is
described within the QCD dipole formalism. Realistic quarkonium wave functions
in the $Q\bar Q$ rest frame are calculated by solving the Schr\"odinger
equation with a subsequent Lorentz boost to high energy. We rely on several
realistic $Q\bar Q$ potentials, which allow to describe well the quarkonium
masses and decay widths, as well as data on diffractive electroproduction of
quarkonia on protons. Nuclear effects are calculated with the phenomenological
dipole cross sections fitted to DIS data. The higher twist quark shadowing
related to the lowest $Q\bar Q$ Fock component of the photon, as well as the
leading twist gluon shadowing, related to higher components containing gluons,
are included. The results for coherent and incoherent photoproduction of
charmonia and bottomonia in UPC of heavy nuclei are in good accord with
available data from the LHC. They can also be verified in future experiments at
electron-ion colliders.
