Let $D$ be the open unit disc. It is known that there are holomorphic functions $f$ on $D$ for which the partial sums $(S_n(f))$ of the Taylor series about 0 have universal approximation properties on every compact set with connected complement outside $D$. It is known, also, that the previous result fails when we consider the sequence $B_n(S_n(f))$ instead of $(S_n(f))$ where $(B_n)$ is an arbitrary sequence of complex numbers. However we can satisfy universal approximation properties on some specific compact sets. We give, in this talk, specific examples of sequences and compact sets in which the previous results holds.