  We present results on the effects of spin-orbit coupling on the electronic
structure of few-electron interacting quantum dots. The ground-state properties
as a function of the number of electrons in the dot $N$ are calculated by means
of spin density functional theory. We find a suppression of Hund's rule due to
the competition of the Rashba effect and exchange interaction. Introducing an
in-plane Zeeman field leads to a paramagnetic behavior of the dot in a closed
shell configuration, and to spin texture in space.
