  Using a recent Mergelyan type theorem, we show the existence of universal
Taylor series on products of planar simply connected domains Oi that extend
continuously on the product of the union of Oi with Si , where Si are subsets
of the boundary of Oi, open in the relative topology. The universal
approximation occurs on every product of compact sets Ki such that C - Ki are
connected and for some i0 it holds that Ki0 is contained in the complement of
the union of Oi0 with the closure of Si0. Furthermore,we introduce some
topological properties of universal Taylor series that lead to the voidance of
some families of functions.
