  In this paper, we describe the moduli space of rank three parabolic
logarithmic connections on the projective line with three poles for any local
exponents. In particular, we show that the family of moduli spaces of rank
three parabolic $\phi$-connections on the projective line with three poles is
isomorphic to the family of $A^{(1)*}_2$-surfaces in Sakai's classification of
Painlev\'e equations. Through this description, we investigate the relation
between the apparent singularities and underlying parabolic bundles.
