  We find an exact solution for the problem of electron spin relaxation in a 2D
circle with Rashba spin-orbit interaction. Our analysis shows that the spin
relaxation in finite-size regions involves three stages and is described by
multiple spin relaxation times. It is important that the longest spin
relaxation time increases with decrease in system radius but always remains
finite. Therefore, at long times, the spin polarization in small 2D systems
decays exponentially with a size-dependent rate. This prediction is supported
by results of Monte Carlo simulations.
