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Electronic shell structure and spin effects in deformed quantum dots are investigated using spin-density functional theory. We recently suggested (Koskinen et al., Phys. Rev. Lett. 79 (1997) 1389) that for circular dots, depending on the density of the two-dimensional electron gas and the electron number, a spin-density wave-like state can occur as a possible ground state. Here these studies are extended to deformed and superdeformed dots, which approach the limit of a finite quantum wire.