  Context. Classical novae are thermonuclear explosions that take place in the
envelopes of accreting white dwarfs in stellar binary systems. The material
transferred onto the white dwarf piles up under degenerate conditions, driving
a thermonuclear runaway. In those outbursts, about 10-7 - 10-3 Msun, enriched
in CNO and, sometimes, other intermediate-mass elements (e.g., Ne, Na, Mg, or
Al, for ONe novae) are ejected into the interstellar medium. The large
concentrations of metals spectroscopically inferred in the nova ejecta reveal
that the (solar-like) material transferred from the secondary mixes with the
outermost layers of the underlying white dwarf.
  Aims. Most theoretical models of nova outbursts reported to date yield, on
average, outflows characterized by O > C, from which only oxidized condensates
(e.g, O-rich grains) would be expected, in principle.
  Methods. To specifically address whether CO novae can actually produce C-rich
dust, six different hydrodynamic nova models have been evolved, from accretion
to the expansion and ejection stages, with different choices for the
composition of the substrate with which the solar-like accreted material mixes.
Updated chemical profiles inside the H-exhausted core have been used, based on
stellar evolution calculations for a progenitor of 8 Msun through H and
He-burning phases.
  Results. We show that these profiles lead to C-rich ejecta after the nova
outburst. This extends the possible contribution of novae to the inventory of
presolar grains identified in meteorites, particularly in a number of
carbonaceous phases (i.e., nanodiamonds, silicon carbides and graphites).
