We apply the microscopic. polymer reference interaction site model integral equation theory to study the structure and phase behavior of spherical nanopaiticles wit h six symmetrically grafted chains in,I homopolymer matrix that is chemically identical to the grafted polymer Calculations of the particle-particle potential of mean force (PM F), Pair correlation functions, and collective structure factors under athermal conditions and in the presence interfiller attractions are presented Polymer grafted nanoparticles disperse or aggregate in the homopolymer matrix depending oil how much of the filler surface is effectively covered by the tethered chains which sterically shield direct intercore attractions If the nanoparticle volume is less than its total tether analogue, the Filler sui face is well shielded and nanoparticles tend to disperse. For smaller filler cores (similar to 2 nm) the grafting density is more brush-like, and the PMF becomes more attractive at contact with increasing matrix chain length due to decreasing wettability of the tether layer For larger particles with much lower grafting density. the effect of matrix chain length oil the PMF is different, ,and for all matrix lengths, the PMF at contact call be switched from attractive to icpulsive by increasing the grafted chain length At nonzero filler concentiations, nanoparticles with tether volume matching the filler cote volume exhibit a critical attraction strength below which repulsive forces dominate resulting in good dispersion. Above the critical attraction strength, enthalpre effects dominate and the PM F becomes increasing attraciive at contact and favors nanoparticle aggregation. When the tether and matrix chain lengths are equal, as the nanoparlicle size increases less of its surface is shielded and modest clustering occurs due to direct core-core attraction and matrix-induced depletion attraction. The microphase spmodal temperature of nanoparticles with six grafted chains monotonically decreases upon homopolymer addition ("dilution "behavior), while nancparticles with only one or two grafted chains exhibit subtle competition between dilution and matrix-mediated depletion attraction that increases their microphase separation temperature.