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Numerical Monte Carlo studies and analytical considerations are reported, indicating that in certain models of multilayer irreversible surface adsorption the density may actually increase away from the substrate. This unexpected conclusion is contrary to simple intuitive considerations in the formation of amorphous deposits. The behavior of the density is found to obey a universal power law. Some timedependent properties are also examined. PACS number(s): 05.70.Ln, 68.1O.Jy, 82.20.Wtdoi:10.1103/physreva.45.6099 pmid:9907709 fatcat:qah5wfb625fidkjb2ffamwqeda