  Polycyclic aromatic hydrocarbons (PAHs) and fullerenes play a major role in
the physics and chemistry of the interstellar medium. Based on a number of
recent experimental and theoretical investigations we developed a model in
which PAHs are subject to photo-dissociation (carbon and hydrogen loss) and
hydrogenation. We take into account that dehydrogenated PAHs may fold into
closed structures -- fullerenes. Fullerenes, in their turn, can be also
hydrogenated, becoming fulleranes, and photo-dissociated, losing carbon and
hydrogen atoms. The carbon loss leads to shrinking of fullerene cages to
smaller ones. We calculate the abundance of PAHs and fullerenes of different
sizes and hydrogenation level depending on external conditions: the gas
temperature, intensity of radiation field, number density of hydrogen atoms,
carbon atoms, and electrons. We highlight the conditions, which are favourable
for fullerene formation from PAHs, and we conclude that this mechanism works
not only in H-poor environment but also at modest values of hydrogen density up
to 10$^{4}$~cm$^{-3}$. We found that fulleranes can be formed in the ISM,
although the fraction of carbon atoms locked in them can be maximum around
10$^{-9}$. We applied our model to two photo-dissociation regions, Orion Bar
and NGC 7023. We compare our estimates of the fullerene abundance and synthetic
band intensities in these objects with the observations and conclude that our
model gives good results for the closest surroundings of ionising stars. We
also demonstrate that additional fullerene formation channels should operate
along with UV-induced formation to explain abundance of fullerenes far from UV
sources.
