Linear flexible polymers end-grafted onto the spherical surface ("hairy sphere") are simulated using the cooperative motion algorithm. The simulations are performed in two extremes of the surrounding matrix: (1) The hairy sphere immersed in a pure solvent of single beads and (2) the hairy sphere in a melt of linear chains. The static properties of the grafted chains are analyzed by calculating the polymer concentration profiles, the distributions of polymer centers-of-mass and of the free chain ends for various values of the sphere radius, various chain lengths, and variable coverage of the sphere surface by the grafting-chain ends (surface coverage). Ordering phenomena of the polymers and their intramolecular structure are taken into account by considering the orientation correlation parameter, the mean-squared radius of gyration and the mean-squared end-to-end distance as functions of the position of the polymer centers-of-mass with respect to the sphere surface. In case (2) some properties of the melt chains have also been analyzed. The simulations indicate that (1) the concentration profiles of the end-grafted chains under good solvent conditions are noticeably different from those in a melt, (2) in both cases, they are strongly affected by the values of the surface coverage, (3) as the sphere radius increases, the monomer concentration profile changes from concave to convex, (4) both the free ends and the centers of mass of the grafted chains reveal a tendency to concentrate at some distance from the surface, i.e., the profiles have noticeable maxima, (5) for small surface coverage the chain centers of mass penetrate into the sphere, especially when anchored to the smaller sphere in the melt, (6) depending on the position of the center-of-mass of the end-grafted chains, both tangential and radial ordering of the polymers relative to the sphere exists, (7) the end-to-end vectors and radii of gyration show a paraboliclike shape with minima at a finite distance from the surface. (C) 2003 American Institute of Physics.