Nanoparticles tend to agglomerate. The process of agglomeration is ruled by thermodynamics. Depending on the sign of the enthalpy of interaction, ensembles consist of (repelling) poorly agglomerated or (attracting) highly agglomerated particles. For these two cases different distribution functions for the agglomerates were found. The size distribution of the agglomerates is ruled by the maximum of the entropy of the ensemble of agglomerates, which is calculated using Gibbs formula of entropy. The exact determination of the size distribution of the agglomerates also gives the maximum size of the agglomerates. These considerations lead to an improved understanding of ensembles of agglomerated nanoparticles.