The question of the dominant interparticle magnetic interaction type in random closely packed assemblies of different diameter (6.2-11.5 nm) bare maghemite nanoparticles (NPs) is addressed. Single-particle magnetic properties such as particle anisotropy and exchange bias field are first of all studied in dilute (reference) systems of these same NPs, where interparticle interactions are neglible. Substantial surface spin disorder is revealed in all particles except the smallest, viz. for diameters d = 8-11.5 nm but not for d = 6.2-6.3 nm. X-ray diffraction analysis points to a crystallographic origin of this effect. The study of closely packed assemblies of the d ≥ 8 nm particles observes collective (superspin) freezing that clearly appears to be governed by interparticle dipole interactions. However, the dense assemblies of the smallest particles exhibit freezing temperatures that are higher than expected from a simple (dipole) extrapolation of the corresponding temperatures found in the d ≥ 8 nm assemblies. It is suggested that the nature of the dominant interparticle interaction in these smaller particle assemblies is superexchange, whereby the lack of significant surface spin disorder allows this mechanism to become important at the level of interacting superspins.