  Generic Painlev\'e VI tau function \tau(t) can be interpreted as four-point
correlator of primary fields of arbitrary dimensions in 2D CFT with c=1. Using
AGT combinatorial representation of conformal blocks and determining the
corresponding structure constants, we obtain full and completely explicit
expansion of \tau(t) near the singular points. After a check of this expansion,
we discuss examples of conformal blocks arising from Riccati, Picard, Chazy and
algebraic solutions of Painlev\'e VI.
