The kinetics of irreversible multilayer deposition on onehyphen; and twohyphen;dimensional uniform substrates was studied. It was assumed that the distribution of sizes of parking objects, intervals in 1D and disks in 2D, have a smallhyphen;size and a largehyphen;size cutoff,landL, respectively. The general case when the parking distribution function varies as (xminus;l)agr;near the smallhyphen;size cutoff was studied. It was found that the coverage in each layer approaches to the jamming limit according to a power law astminus;ngr;, with the exponent ngr;=(agr;+1+D)minus;1. The jamming coverages approach the infinitehyphen;layer limiting value exponentially as exp(minus;k/s), with the correlation lengths=lnlsqb;(agr;+3)/(agr;+1)rsqb;.
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