  We model the late evolution and mass loss history of rapidly rotating
Wolf-Rayet stars in the mass range $5\,\rm{M}_{\odot}\dots
100\,\rm{M}_{\odot}$. We find that quasi-chemically homogeneously evolving
single stars computed with enhanced mixing retain very little or no helium and
are compatible with Type\,Ic supernovae. The more efficient removal of core
angular momentum and the expected smaller compact object mass in our lower mass
models lead to core spins in the range suggested for magnetar driven
superluminous supernovae. Our more massive models retain larger specific core
angular momenta, expected for long-duration gamma-ray bursts in the collapsar
scenario. Due to the absence of a significant He envelope, the rapidly
increasing neutrino emission after core helium exhaustion leads to an
accelerated contraction of the whole star, inducing a strong spin-up, and
centrifugally driven mass loss at rates of up to
$10^{-2}\,\rm{M}_{\odot}~\rm{yr^{-1}}$ in the last years to decades before core
collapse. Since the angular momentum transport in our lower mass models
enhances the envelope spin-up, they show the largest relative amounts of
centrifugally enforced mass loss, i.e., up to 25\% of the expected ejecta mass.
Our most massive models evolve into the pulsational pair-instability regime. We
would thus expect signatures of interaction with a C/O-rich circumstellar
medium for Type~Ic superluminous supernovae with ejecta masses below $\sim
10\,\rm{M}_{\odot}$ and for the most massive engine-driven explosions with
ejecta masses above $\sim 30\,\rm{M}_{\odot}$. Signs of such interaction should
be observable at early epochs of the supernova explosion, and may be related to
bumps observed in the light curves of superluminous supernovae, or to the
massive circumstellar CO-shell proposed for Type~Ic superluminous supernova
Gaia16apd.
