  We show that the fractional statistics of quasiparticles in dimerized
graphene, in recent proposals for charge and statistics fractionalization, can
have two realizations depending whether elementary objects can be considered as
point-like or extended objects. Therefore, there are two phases of proposed
excitations and we give their topological descriptions with their respective
statistics. We propose that a natural setting for fractionalization are certain
systems with excitonic instabilities and demonstrate this by an example of
graphene bilayer.
