Wild globally hyperbolic maximal anti-de Sitter structures

Let (Formula presented.) be a connected, oriented surface with punctures and negative Euler characteristic. We introduce wild globally hyperbolic anti-de Sitter structures on (Formula presented.) and provide two parameterisations of their deformation space: as a quotient of the product of two copies of the Teichmüller space of crowned hyperbolic surfaces and as the bundle over the Teichmüller space of (Formula presented.) of meromorphic quadratic differentials with poles of order at least 3 at the punctures.