The processes underlying formation and growth of unfolded protein inclusions are relevant to neurodegenerative diseases but poorly characterized in living cells. In S. cerevisiae, inclusions formed by mutant huntingtin (mHtt) have some characteristics of biomolecular condensates but the physical nature and growth mechanisms of inclusion bodies remain unclear. We have probed the relationship between concentration and inclusion growth in vivo and find that growth of mHtt inclusions in living cells is triggered at a cytoplasmic threshold concentration, while reduction in cytoplasmic mHtt causes inclusions to shrink. The growth rate is consistent with incorporation of new material through collision and coalescence. A small remnant of the inclusion is relatively long-lasting, suggesting that it contains a core that is structurally distinct, and which may serve to nucleate it. These observations support a model in which aggregative particles are incorporated by random collision into a phase-separated condensate composed of a particle-rich mixture.