  The goal of this research is to study how the fragmentation of planetary
embryos can affect the physical and dynamical properties of terrestrial planets
around solar-type stars. Our work focuses on the formation and evolution of
planets and water delivery in the Habitable Zone. We distinguish class A and
class B HZ planets, which have an accretion seed initially located inside and
beyond the snowline, respectively. We develop an Nbody integrator that
incorporates fragmentation and hit-and-run collisions, which is called D3
N-body code. From this, we perform 46 numerical simulations of planetary
accretion in systems that host two gaseous giants like Jupiter and Saturn. We
compare two sets of 23 N-body simulations, one of which includes a realistic
collisional treatment and the other one models all impacts as perfect mergers.
The final masses of the HZ planets formed in runs with fragmentation are about
15\%-20\% smaller than those obtained without fragmentation. As for the class A
HZ planets, those formed in simulations without fragmentation experience very
significant increases in mass respect to their initial values, while the growth
of those produced in runs with fragmentation is less relevant. We remark that
the fragments play a secondary role in the masses of the class A HZ planets,
providing less than 30\% of their final values. In runs without fragmentation,
the final fraction of water of the class A HZ planets keeps the initial value
since they do not accrete water-rich embryos. In runs with fragmentation, the
final fraction of water of such planets strongly depends on the model used to
distribute the water after each collision. The class B HZ planets do not show
significant differences concerning their final water contents in runs with and
without fragmentation. From this, we find that the collisional fragmentation is
not a barrier to the survival of water worlds in the HZ.
