In this paper, we apply a reformulated version of the Surface Equivalence Principle, originally defined for radiating phenomena in terms of tangential fields, to cloaking problems in terms of admittance functions at an arbitrary boundary. In order to cloak a dielectric/metallic object, the tangential fields ratio (admittance) can be controlled at any arbitrary attached/detached surface boundary. The dispersive surface admittance cloak, as originally introduced for Mantle Cloaking, is computed in a closed-form solution at any frequency regime (quasi-static and beyond).