We examine minimizers for the Landau - de Gennes energy in a slab $\Omega\times (−\delta,\delta)$ where the cross section $\Omega$ is a bounded simply connected domain in $\mathbb{R}^2$. The minimizers are to satisfy tangential boundary conditions on the top and bottom faces and prescribed boundary conditions on the lateral surface. We determine the defect structures, textures and estimates on the energies for minimizers. In particular it is shown how these features depend on the relative sizes of the Landau - de Gennes order parameter $\varepsilon$ and the slab thickness $2\delta$. This is joint work with Patricia Bauman.