Generic power series on subsets of the unit disk

In this paper, we examine the boundary behaviour of generic power series $f$ with coefficients chosen from a fixed bounded set $\Lambda$ in sense Baire category. Notably, prove that for any open subset $U$ unit disk $D$ non-real point on circle, $f(U)$ is dense $\CC$. As it demonstrated, conclusion does not necessarily hold arbitrary sets accumulating to circle. To complement these results, characterization coefficient having property given.