  Understanding the formation of the extremely metal poor star
SDSS-J102915+172927 is of fundamental importance to improve our knowledge on
the transition between the first and second generation of stars in the
Universe. In this paper, we perform three-dimensional cosmological
hydrodynamical simulations of dust-enriched halos during the early stages of
the collapse process including a detailed treatment of the dust physics. We
employ the astrochemistry package \krome coupled with the hydrodynamical code
\textsc{enzo} assuming grain size distributions produced by the explosion of
core-collapse supernovae of 20 and 35 M$_\odot$ primordial stars which are
suitable to reproduce the chemical pattern of the SDSS-J102915+172927 star. We
find that the dust mass yield produced from Population III supernovae
explosions is the most important factor which drives the thermal evolution and
the dynamical properties of the halos. Hence, for the specific distributions
relevant in this context, the composition, the dust optical properties, and the
size-range have only minor effects on the results due to similar cooling
functions. We also show that the critical dust mass to enable fragmentation
provided by semi-analytical models should be revised, as we obtain values one
order of magnitude larger. This determines the transition from disk
fragmentation to a more filamentary fragmentation mode, and suggests that
likely more than one single supernova event or efficient dust growth should be
invoked to get such a high dust content.
