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In this paper, we describe the moduli space of rank three paraboliclogarithmic connections on the projective line with three poles for any localexponents. In particular, we show that the family of moduli spaces of rankthree parabolic phi-connections on the projective line with three poles isisomorphic to the family of A^{(1)*}_2-surfaces in Sakai's classification ofPainlev\'e equations. Through this description, we investigate the relationbetween the apparent singularities and underlying parabolic bundles. In anappendix, we also describe the moduli space of parabolic Higgs bundles of theabove setting and the Hitchin fibration.

Moduli space of rank three logarithmic connections on the projective line with three poles