  A holomorphic function f on a simply connected domain {\Omega} is said to
possess a universal Taylor series about a point in {\Omega} if the partial sums
of that series approximate arbitrary polynomials on arbitrary compacta K
outside {\Omega} (provided only that K has connected complement). This paper
shows that this property is not conformally invariant, and, in the case where
{\Omega} is the unit disc, that such functions have extreme angular boundary
behaviour.
