How does an initially homogeneous spin polarization in a confined two-dimensional electron gas with Rashba spin-orbit coupling evolve in time? How does the relaxation time depend on system size? We study these questions for systems of a size that is much larger than the Fermi wavelength, but comparable and even shorter than the spin relaxation length. Depending on the confinement spin relaxation may become faster or slower than in the bulk. An initially homogeneously polarized spin system evolves into a spiral pattern.