A star-shaped polymer whose center unit is adsorbed on a surface offers a peculiar example of surface-grafted polymers. When it is isolated in a good solvent, it has been conjectured that several distinct scaling relations hold for the monomer and end-point density profiles. Especially, the density decay in a direction parallel to the surface is described by a new critical exponent λ(f) as ρ(r,z = 0) ∼ r-d+λ(f). However, the precise values of the exponent as a function of the number of arms were still unclear. Another interesting quantity is the total number of configurations behaving as N ∼ lγs(f)-1 μfl. Here, l is the length of the arm, μ the effective coordination number for a single chain, and λs(f) a new surface critical exponent yet to be known. We perform large scale Monte Carlo simulations of such an adsorbed star with the number of arms, f, ranging from 2 to 15, to verify the predicted scaling theory and to calculate various static properties and exponents. Estimates of γs(f) are presented. The validity of the scaling relations is clearly shown, and the first estimation of the value of λ(f) is given also. Furthermore, an empirical form of the exponent λ(f) as a function of f is proposed.
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