The spin-Hall effect is about the generation of a transverse pure spin current by an electrical charge current as a consequence of spin-orbit interaction in, e.g., semiconductors. This spin current in turn can generate a detectable electric field (inverse spin-Hall effect). In our proposal we plan to explore the spin-Hall effect in three (3D) and two-dimensional (2D) hole systems. By employing p-epilayers and high mobility 2D hole systems (2DHS) in GaAs based heterojunctions we focus on three geometries, the H-geometry , the spin-injection-geometry and a Hall bar geometry to probe the spin-Hall effect electrically. For the last phase of this Priority Program we put emphasis especially on the latter two geometries. Here, the Hall geometry is a new additional geometry which can be considered is an electrical analogue of Awschalom’s optical experiments.