We present the results of a theoretical study of internal microstructures in two-dimensional ferrofluids without an external magnetic field. Recent experiments with these systems demonstrate the appearance of linear chains and ringlike and various branched clusters. We consider linear chains, rings, and branched Y-like "forks." In the model of an ideal gas of noninteracting clusters, taking into ... [Show full abstract] account interactions only between nearest particles, we estimate the equilibrium distribution functions of the chains, forks, and rings over a number of particles in them. Our results show that for experimentally realistic situations the majority of particles are united into chains and forks, the number of particles in the rings being relatively small. The results of calculations are in qualitative agreement with experiments.