Heavy quarks are copiously produced in ultra-peripheral heavy ion collisions. In the strong electromagnetic fields, cc and bb are produced by photonuclear and two-photon interactions; hadroproduction can occur in grazing interactions. We present the total cross sections, quark transverse momentum and rapidity distributions, as well as the QQ invariant mass spectra from the three production channels. We consider AA and pA collisions at the Relativistic Heavy Ion Collider and Large Hadron Collider. We discuss techniques for separating the three processes and describe how the AA to pA production ratios might be measured accurately enough to study nuclear shadowing. I
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