We study the spin relaxation (SR) of a two-dimensional electron gas (2DEG) in the quantized Hall regime and discuss the role of spatial inhomogeneity effects on the relaxation. The results are obtained for small filling factors ($ ull 1$) or when the filling factor is close to an integer. In either case SR times are essentially determined by a smooth random potential. For small $ u$ we predict a magneto-confinement resonance manifested in the enhancement of the SR rate when the Zeeman energy is close to the spacing of confinement sublevels in the low-energy wing of the disorder-broadened Landau level. In the resonant region the $B$-dependence of the SR time has a peculiar non-monotonic shape. If $ usimeq 2n+1$, the SR is going non-exponentially. Under typical conditions the calculated SR times range from $10^{-8}$ to $10^{-6} $s.
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