Phantom chain simulations can be utilized for studying the molecular arrangements in systems of chain molecules filled with randomly distributed solid nanoparticles, provided that the interaction energy between chains and filler is modified in order to counterbalance the intrinsic tendency of the chain segments to avoid the filler surfaces. In fact, all properties of systems containing phantom chains with suitably modified interactions of this kind are found to be in excellent agreement with those previously obtained for dense systems having the same composition. This makes possible to study systems that cannot be simulated at full density (i.e., systems with long chains and/or with large particles and small filling density). Simulations performed for long phantom chains show that the simple rules recently proposed to predict the mutual arrangements of particles and chains in the dense systems simulated up to now can be extended to very long chains. However, these rules should be modified in order to be valid also for large particles and small filling density.