  The theory of universal Taylor series can be extended to the case of Pad\'e
approximants where the universal approximation is not realized by polynomials
any more, but by rational functions, namely the Pad\'e approximants of some
power series. We present the first generic result in this direction, for Pad\'e
approximants corresponding to Taylor developments of holomorphic functions in
simply connected domains. The universal approximation is required only on
compact sets $K$ which lie outside the domain of definition and have connected
complement. If the sets $K$ are additionally disjoint from the boundary of the
domain of definition, then the universal functions can be smooth on the
boundary.
