  (Abridged abstract) We explore the formation of ultra-massive (M_{\rm WD}
\gtrsim 1.05 M_\sun$), carbon-oxygen core white dwarfs resulting from single
stellar evolution. We also study their evolutionary and pulsational properties
and compare them with those of the ultra-massive white dwarfs with oxygen-neon
cores resulting from carbon burning in single progenitor stars, and with binary
merger predictions. We consider two single-star evolution scenarios for the
formation of ultra-massive carbon-oxygen core white dwarfs that involve
rotation of the degenerate core after core helium burning and reduced mass-loss
rates in massive asymptotic giant-branch stars. We compare our findings with
the predictions from ultra-massive white dwarfs resulting from the merger of
two equal-mass carbon-oxygen core white dwarfs, by assuming complete mixing
between them and a carbon-oxygen core for the merged remnant. The resulting
ultra-massive carbon-oxygen core white dwarfs evolve markedly slower than their
oxygen-neon counterparts. Our study strongly suggests the formation of
ultra-massive white dwarfs with carbon-oxygen core from single stellar
evolution. We find that both the evolutionary and pulsation properties of these
white dwarfs are markedly different from those of their oxygen-neon core
counterparts and from those white dwarfs with carbon-oxygen core that might
result from double degenerate mergers. This can eventually be used to discern
the core composition of ultra-massive white dwarfs and their formation
scenario.
