We compute the phase diagram of the simplest holographic bottom-up model of conformal interfaces. The model consists of a thin domain wall between three-dimensional Anti-de Sitter (AdS) vacua, anchored on a boundary circle. We distinguish five phases depending on the existence of a black hole, the intersection of its horizon with the wall, and the fate of inertial observers. We show that, like the Hawking-Page phase transition, the capture of the wall by the horizon is also a first order transition and comment on its field-theory interpretation. The static solutions of the domain-wall equations include gravitational avatars of the Faraday cage, black holes with negative specific heat, and an intriguing phenomenon of suspended vacuum bubbles corresponding to an exotic interface/anti-interface fusion. Part of our analysis overlaps with recent work by Simidzija and Van Raamsdonk but the interpretation is different.