  Let $\Sigma$ be a connected, oriented surface with punctures and negative
Euler characteristic. We introduce wild globally hyperbolic anti-de Sitter
structures on $\Sigma \times \mathbb{R}$ and provide two parameterisations of
their deformation space: as a quotient of the product of two copies of the
Teichm\"uller space of crowned hyperbolic surfaces and as the bundle over the
Teichm\"uller space of $\Sigma$ of meromorphic quadratic differentials with
poles of order at least $3$ at the punctures.
