  In this paper, we classify all (complete) non elementary algebraic solutions
of Garnier systems that can be constructed by Kitaev's method: they are deduced
from isomonodromic deformations defined by pulling back a given fuchsian
equation E by a family of ramified covers. We first introduce orbifold
structures associated to a fuchsian equation. This allow to get a refined
version of Riemann-Hurwitz formula and then to promtly deduce that E is
hypergeometric. Then, we can bound exponents and degree of the pull-back maps
and further list all possible ramification cases. This generalizes a result due
to C. Doran for the Painleve VI case. We explicitely construct one of these
solutions.
