  Existence of solutions to a $\Phi$-Laplacian singular system is obtained via
shifting method and variational methods. A priori estimates are furnished
through De Giorgi's technique, Talenti's rearrangement argument, and exploiting
the weak Harnack inequality, while decay of solutions is obtained via
comparison with radial solutions to auxiliary problems. Finally, uniqueness is
investigated, and a Diaz-Saa type result is provided.
