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We develop a new fast-diffusion approximation for the kinetics of depositionof extended objects on a linear substrate, accompanied by diffusionalrelaxation. This new approximation plays the role of the mean-field theory forsuch processes and is valid over a significantly larger range than an earliervariant, which was based on a mapping to chemical reactions. In particular,continuum-limit off-lattice deposition is described naturally within ourapproximation. The criteria for the applicability of the mean-field theory arederived. While deposition of dimers, and marginally, trimers, is affected byfluctuations, we find that the k-mer deposition kinetics is asymptoticallymean-field like for all k=4,5,..., where the limit k->infinity, when properlydefined, describes deposition-diffusion kinetics in the continuum.Comment: 18 page

Random sequential adsorption on a line: Mean-field theory of diffusional relaxation