This paper investigates the geometry and physics of quasi-local horizons (QLHs) and their relation to structures at null infinity $ J^{+} $. It focuses on Weakly Isolated Horizons (WIHs), which are defined as null 3-dimensional sub-manifolds with specific geometric properties. The paper shows that $ J^{+} $, the boundary of the Penrose conformal completion of an asymptotically flat space-time, is a WIH in the conformal completion $ (\hat{M}, \hat{g}_{ab}) $, not in the physical space-time $ (M, g_{ab}) $. This distinction leads to different physical interpretations: while black hole (or cosmological) WIHs $ \Delta $ are sub-manifolds of the physical space-time and have no flux of gravitational radiation, $ J^{+} $ is a WIH in the conformal completion and has a non-zero flux of radiation. The paper demonstrates that the BMS group at $ J^{+} $ arises from the symmetry group of WIHs. It also shows that the universal structure and symmetry groups of WIHs are the same for both $ \Delta $ and $ J^{+} $, but the physics they capture is different. The paper concludes that the difference in physics is due to the different field equations satisfied by $ g_{ab} $ and $ \hat{g}_{ab} $, leading to different time dependencies of the intrinsic connection $ D $ and different degrees of freedom in the geometry. The paper also discusses the implications of these results for the study of black hole evaporation in quantum gravity.This paper investigates the geometry and physics of quasi-local horizons (QLHs) and their relation to structures at null infinity $ J^{+} $. It focuses on Weakly Isolated Horizons (WIHs), which are defined as null 3-dimensional sub-manifolds with specific geometric properties. The paper shows that $ J^{+} $, the boundary of the Penrose conformal completion of an asymptotically flat space-time, is a WIH in the conformal completion $ (\hat{M}, \hat{g}_{ab}) $, not in the physical space-time $ (M, g_{ab}) $. This distinction leads to different physical interpretations: while black hole (or cosmological) WIHs $ \Delta $ are sub-manifolds of the physical space-time and have no flux of gravitational radiation, $ J^{+} $ is a WIH in the conformal completion and has a non-zero flux of radiation. The paper demonstrates that the BMS group at $ J^{+} $ arises from the symmetry group of WIHs. It also shows that the universal structure and symmetry groups of WIHs are the same for both $ \Delta $ and $ J^{+} $, but the physics they capture is different. The paper concludes that the difference in physics is due to the different field equations satisfied by $ g_{ab} $ and $ \hat{g}_{ab} $, leading to different time dependencies of the intrinsic connection $ D $ and different degrees of freedom in the geometry. The paper also discusses the implications of these results for the study of black hole evaporation in quantum gravity.