We study relative Cohn path algebras, also known as Leavitt-Cohn path algebras, and we realize them as partial skew group rings. To do this we prove uniqueness theorems for relative Cohn path algebras. Furthermore, given any graph E we define E-relative branching systems and prove how they induce representations of the associated relative Cohn path algebra. We give necessary and sufficient conditions for faithfulness of the representations associated to E-relative branching systems. This
improves previous results known to Leavitt path algebras of row-finite graphs with no sinks. To prove this last result we show first a version, for relative Cohn-path algebras, of the reduction theorem for Leavitt path algebras.
