  Ultra-massive white dwarfs ($\rm M_{WD} \gtrsim 1.05\, M_{\odot}$) are
considered powerful tools to study type Ia supernovae explosions, merger
events, the occurrence of physical processes in the Super Asymptotic Giant
Branch (SAGB) phase, and the existence of high magnetic fields. Traditionally,
ultra-massive white dwarfs are expected to harbour oxygen-neon (ONe) cores.
However, new observations and recent theoretical studies suggest that the
progenitors of some ultra-massive white dwarfs can avoid carbon burning,
leading to the formation of ultra-massive white dwarfs harbouring carbon-oxygen
(CO) cores. Here we present a set of ultra-massive white dwarf evolutionary
sequences with CO cores for a wide range of metallicity and masses. We take
into account the energy released by latent heat and phase separation during the
crystallization process and by $^{22}$Ne sedimentation. Realistic chemical
profiles resulting from the full computation of progenitor evolution are
considered. We compare our CO ultra-massive white dwarf models with ONe models.
We conclude that CO ultra-massive white dwarfs evolve significantly slower than
their ONe counterparts mainly for three reasons: their larger thermal content,
the effect of crystallization, and the effect of $^{22}$Ne sedimentation. We
also provide colors in several photometric bands on the basis of new model
atmospheres. These CO ultra-massive white dwarf models, together with the ONe
ultra-massive white dwarf models, provide an appropriate theoretical framework
to study the ultra-massive white dwarf population in our Galaxy.
