  We study within the framework of the Lifshitz theory the long-range Casimir
force for in-plane isotropic and anisotropic free-standing transdimensional
material slabs. In the former case, we show that the confinement-induced
nonlocality not only weakens the attraction of ultrathin slabs but also changes
the distance dependence of the material-dependent correction to the Casimir
force to go as $\sim\!1/\!\sqrt{l}$ contrary to the $\sim\!1/l$ dependence of
that of the local Lifshitz force. In the latter case, we use closely packed
array of parallel aligned single-wall carbon nanotubes in a dielectric layer of
finite thickness to demonstrate strong orientational anisotropy and crossover
behavior for the inter-slab attractive force in addition to its reduction with
decreasing slab thickness. We give physical insight as to why such a pair of
ultrathin slabs prefers to stick together in the perpendicularly oriented
manner, rather than in the parallel relative orientation as one would
customarily expect.
