We describe pair-production models of spin-0 and spin-1/2 magnetic monopoles and high-electric-charge objects in proton-proton and heavy-ion collisions, considering both the Drell-Yan and the photon-fusion processes. In particular, we extend the Drell-Yan production model of spin-1/2 high-electric-charge objects to include $Z^0$-boson exchange for proton-proton collisions. Furthermore, we explore spin-1/2 and, for the first time, spin-0 production in ultraperipheral heavy-ion collisions. With matrix element calculations and equivalent photon fluxes implemented in MadGraph5_aMC@NLO, we present leading-order production cross sections of these mechanisms in $sqrt{s} = 14$ TeV proton-proton collisions and $sqrt{s_{text{NN}}} = 5.5$ TeV ultraperipheral lead-lead collisions at the LHC. While the mass range accessible in ultraperipheral lead-lead collisions is much lower than that in proton-proton collisions, we find that the theoretical production cross sections are significantly enhanced in the former for masses below 82 GeV.
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