The paper discusses the Karch-Randall braneworld, a setup that allows for the study of Hawking radiation from a black hole using holographic tools. The black hole lives on a brane and is highly quantum, but has a holographic dual as a higher-dimensional classical theory in the ambient space. The black hole is coupled to a nongravitational bath, which absorbs its Hawking radiation. The entropy of the Hawking radiation can be computed by studying the bath using the quantum extremal surface prescription, which geometricizes into a Ryu-Takayanagi surface in the ambient space. The topological phase transition of the Ryu-Takayanagi surface from connecting different portions of the bath to connecting the bath and the brane gives the Page curve of the Hawking radiation, consistent with unitarity. The paper focuses on the case where the ambient space is (2+1)-dimensional, allowing for explicit computations in both the bulk and boundary descriptions. It shows that the topological phase transition of the Ryu-Takayanagi surface corresponds to the formation of a replica wormhole on the Karch-Randall brane, which is the dominant contribution to the replica path integral. For higher-dimensional situations, the geometry of the brane satisfies Einstein's equation coupled with conformal matter. The paper also discusses the implications of these findings for the general rule of gravitational path integral.The paper discusses the Karch-Randall braneworld, a setup that allows for the study of Hawking radiation from a black hole using holographic tools. The black hole lives on a brane and is highly quantum, but has a holographic dual as a higher-dimensional classical theory in the ambient space. The black hole is coupled to a nongravitational bath, which absorbs its Hawking radiation. The entropy of the Hawking radiation can be computed by studying the bath using the quantum extremal surface prescription, which geometricizes into a Ryu-Takayanagi surface in the ambient space. The topological phase transition of the Ryu-Takayanagi surface from connecting different portions of the bath to connecting the bath and the brane gives the Page curve of the Hawking radiation, consistent with unitarity. The paper focuses on the case where the ambient space is (2+1)-dimensional, allowing for explicit computations in both the bulk and boundary descriptions. It shows that the topological phase transition of the Ryu-Takayanagi surface corresponds to the formation of a replica wormhole on the Karch-Randall brane, which is the dominant contribution to the replica path integral. For higher-dimensional situations, the geometry of the brane satisfies Einstein's equation coupled with conformal matter. The paper also discusses the implications of these findings for the general rule of gravitational path integral.