  We study the asymptotic behavior of a size-marked point process of centers of
large cells in a stationary and isotropic Poisson hyperplane mosaic in
dimension $d \ge 2$. The sizes of the cells are measured by their inradius or
their $k$th intrinsic volume ($k \ge 2$), for example. We prove a Poisson limit
theorem for this process in Kantorovich-Rubinstein distance and thereby
generalize a result in Chenavier and Hemsley (2016) in various directions. Our
proof is based on a general Poisson process approximation result that extends a
theorem in Bobrowski, Schulte and Yogeshwaran (2021).
