We discuss the nuclear spin relaxation resulting from molecular translational diffusion of a liquid crystal in the isotropic phase confined to spherical microcavities. The relaxation is induced by the time modulation of spin interactions as molecules diffuse between the ordered surface layer into the isotropic interior volume and back. The calculated spin-lattice relaxation rate T-i(-1) shows three distinct dispersion regimes: a plateau at the lowest frequencies, practically independent of the size of the cavity, an intermediate power-law dispersion regime with an exponent between -0.7 and -1, depending on the spatial profile of the order parameter and cavity radius, and at frequencies above 1 MHz a strong dispersion tending toward the quadratic dependence of the relaxation rate on the Larmor frequency in the high-frequency limit. The pretransitional increase in T-1(-1) depends drastically on the Larmor frequency. The frequency and temperature dependences of T-1(-1) yield not only information on the magnitude of the surface order parameter, but also on its spatial profile, revealing the type of liquid-crystal substrate interactions. Apart from thermotropic liquid crystals in the isotropic phase, this analysis can be also applied to other fluids in porous media. (C) 2004 American Institute of Physics.