Extremal black holes have traditionally been regarded as unphysical objects that cannot arise via gravitational collapse in physically plausible scenarios, a premise long reinforced by the so-called third law of black hole thermodynamics. In the asymptotically flat setting, the third law was disproven in recent work by Kehle and Unger, who applied characteristic gluing techniques to construct solutions to the Einstein–Maxwell-charged scalar field system undergoing gravitational collapse to form an exactly extremal Reissner–Nordström black hole in finite time. In this talk, we explore how these techniques can be extended to include a positive cosmological constant and applied to construct solutions to the Einstein-scalar field system in which an exactly extremal Schwarzschild–de Sitter black hole is formed. We moreover establish that some of these solutions have connected apparent horizons, a feature not possible in the asymptotically flat case. Similarly, we explore the dynamical formation of the related extremal Schwarzschild–de Sitter white hole and Nariai spacetimes.