If a suspension of magnetic micron-sized and nano-sized particles is subjected to a homogeneous magnetic field, the nanoparticles are attracted to the microparticles and form thick anisotropic halos (clouds) around them. Such clouds can hinder approach of microparticles and result in effective repulsion between them [Lopez-Lopez et al. Soft Matter, 6, 4346 (2010)]. In this paper, we present detailed experimental and theoretical studies of nanoparticle concentration profiles and of the equilibrium shapes of nanoparticle clouds around a single magnetized microsphere taking into account interactions between nanoparticles. We show that at strong enough magnetic field, the ensemble of nanoparticles experiences a gas/liquid phase transition such that a dense liquid phase is condensed around the magnetic poles of a microsphere while a dilute gas phase occupies the rest of the suspension volume. Nanoparticle accumulation around a microsphere is governed by two dimensionless parameters – the initial nanoparticle concentration (φ0) and the magnetic-tothermal energy ratio (α) – and the three accumulation regimes are mapped onto a α-φ0 phase diagram. Our local thermodynamic equilibrium approach gives a semi-quantitative agreement with the experiments on equilibrium shapes of nanoparticle clouds. The results of this work could be useful for the development of the bimodal magnetorheological fluids and of the magnetic separation technologies used in bio-analysis and water purification systems.