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

Dynamics of Spin Relaxation in Finite-Size 2D Systems: an Exact Solution