The results of realistic computer simulations of dense polymer melts filled with solid nanoparticles are compared with results obtained for similar systems near planar solid surfaces and with those of Monte Carlo calculations performed for single chains in the presence of spherical solid obstacles. The polymer units at the interface with the filler particles are arranged in densely packed and ordered shells analogous to those found near planar solid surfaces. The polymer chains, reduced in size compared to the unfilled melt, are constituted of sequences of surface segments, totally contained in the interface shell of a given particle, and of bridge segments, connecting different particles. Each chain visits the interface shell of several filler particles, and each particle is in contact with many different polymer chains, such that the filler particles behave as highly functional physical cross-links.