A coarse-grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various polymer lengths, grafting densities, and nanoparticle sizes by molecular dynamics simulations, considering variable solvent quality in the framework of an implicit solvent treatment. Below the theta point, the tuning of the temperature strongly influences the coverage of the nanoparticle surface by collapsed single chains or clusters of several chains. The shape and size of the aggregates depend on the number of monomers and surface density of the polymers. Specifically we analyzed the effect of the solvent quality on the density profiles and radius of gyration of the single molecule. The stretching of the chains parallel to the surface, required for the cluster formation, leads to a slightly non-monotonic temperature variation of the polymer linear dimensions at intermediate chain lengths. For theta conditions, however, the chains are still stretched in the radial direction. In particular for long chains a crossover to the star polymer limit occurs that is studied in detail with self-consistent field theory. At a theoretical level we extended our study exploring the case of a spherical brush embedded in a polymer melt. For different choices of the Flory-Huggins parameter between free and grafted chains, the amount of monomers of the free chains adsorbed on the nanoparticle surface is predicted via self-consistent field calculations.