  We study the spin of the localised quasiparticle excitations of
lowest-Landau-level quantum Hall states defined on a disk. The spin that we
propose satisfies the spin-statistics relation and can be used to reconstruct
the topological geometric phase associated to the exchange of two arbitrarily
chosen quasiparticles. Since it is related to the quadrupole moment of the
quasiparticle charge distribution, it can be measured in an experiment and
could reveal anyonic properties in a way that is complementary to the
interferometric schemes employed so far. We first discuss our definition for
the quasiholes of the Laughlin state, for which we present a numerical and
analytical study of our spin, and we proceed with a discussion of several kinds
of quasiholes of the Halperin 221 state. Finally, we discuss the link between
our spin and the adiabatic rotation of the quasiparticles around their axis and
demonstrate that our spin obeys the spin-statistics relation.
