Localized adsorption of hard (noninteracting) spheroidal particles on homogeneous interfaces was analyzed theoretically. In contrast to previous studies concentrated on flat (side on) adsorption in the present approach an unoriented (quasi-three-dimensional) adsorption of prolate and oblate spheroids was considered. By applying the random sequential adsorption (RSA) approach asymptotic analytic expressions were derived for the available surface function (surface blocking parameter) and adsorption kinetics in the limit of low and moderate surface concentrations. The range of validity of the approximate analytical results was determined by numerical simulations of adsorption kinetics performed using the Monte Carlo RSA technique. It was revealed by this comparison that the analytical approximation can be used with a good accuracy for the dimensionless adsorption time tau smaller than two. The numerical calculations also enabled us to determine the maximum (jamming) surface concentrations for unoriented adsorption of spheroids as a function of the elongation or flattening parameter A. It was demonstrated that these jamming concentrations theta(infinity) are approached for long adsorption times as tau(-1/4), therefore deviating considerably from the Langmuir model used often in the literature.