  Given a vector function ${\bf F}=(F_1,\ldots,F_d),$ analytic on a
neighborhood of some compact subset $E$ of the complex plane with simply
connected complement, we define a sequence of vector rational functions with
common denominator in terms of the expansions of the components $F_k,
k=1,\ldots,d,$ with respect to the sequence of Faber polynomials associated
with $E$. Such sequences of vector rational functions are analogous to row
sequences of type II Hermite-Pad\'e approximation. We give necessary and
sufficient conditions for the convergence with geometric rate of the common
denominators of the sequence of vector rational functions so constructed. The
exact rate of convergence of these denominators is provided and the rate of
convergence of the approximants is estimated. It is shown that the common
denominators of the approximants detect the poles of the system of functions
"closest" to $E$ and their order.
