  In the interstellar medium carbon exists in the form of two stable isotopes
$^{12}$C and $^{13}$C and their ratio is a good indicator of nucleosynthesis in
galaxies. However, chemical fractionation can potentially significantly alter
this ratio and in fact observations of carbon fractionation within the same
galaxy has been found to vary from species to species. In this paper we
theoretically investigate the carbon fractionation for selected abundant
carbon-bearing species in order to determine the conditions that may lead to a
spread of the $^{12}$C/$^{13}$C ratio in external galaxies. We find that carbon
fractionation is sensitive to almost all the physical conditions we
investigated, it strongly varies with time for all species but CO, and shows
pronounced differences across species. Finally we discuss our theoretical
results in the context of the few observations of the $^{12}$C/$^{13}$C ratio
in both local and higher redshift galaxies.
