Universal Taylor series on products of planar domains

Using a recent Mergelyan type theorem for products of planar compact sets, we establish generic existence universal Taylor series on simply connected domains \({\varOmega }_i\), \(i=1,\ldots ,d\). The approximation is realized by partial sums the development function sets \(K_i\), ,d\) such that \({\mathbb {C}}-K_i\) and at least one \(i_0\) set \(K_{i_0}\) disjoint from }_{i_0}\).