Recently, it was shown that by using special artificial materials it is possible to ensure that all electromagnetic modes of free space are conjugately matched to the modes of a material body and, thus, all modes deliver power to the body in the most effective way. Such a fascinating feature is acquired because the conjugate matching does not concern only the propagating modes but, most importantly, is applied to all evanescent modes; in this way, all the possible ways of transferring the electromagnetic energy to the material body can be optimally exploited. However, coupling to higher-order (mostly evanescent) modes is weak and totally disappears in the limit of an infinite planar boundary. Here, we show that by properly perturbing the surface of the receiving or emitting body with, for example, randomly distributed small particles, we can open up channels for super-radiation into the far zone. The currents induced in the small particles act as secondary sources (radiation "vessels") which send the energy to travel far away from the surface and, reciprocally, receive power from far-located sources. For a particular example, we theoretically predict about 20-fold power transfer enhancement between the conjugately matched power-receiving body (as compared with the ideal black body) and far-zone sources. Reciprocally, the proposed structure radiates about 20 times more power into the far zone as compared with the same source over a perfect reflector.