  We present theoretical results with soft-gluon corrections for two separate
processes: (1) the production of a single top quark in association with a $W$
boson in the Standard Model; and (2) the production of a single top quark in
association with a heavy $Z'$ boson in new physics models with or without
anomalous couplings. We show that the higher-order corrections from soft-gluon
emission are dominant for a wide range of collider energies. Results are shown
for the total cross sections and top-quark transverse-momentum and rapidity
distributions for $tW$ and $tZ'$ production at LHC and future collider energies
up to 100 TeV. The uncertainties from scale dependence and parton distribution
functions are also analyzed.
