Aims. We study the production of dust in Type II-P supernova ejecta by coupling the gas-phase chemistry to the dust nucleation and condensation phases. We consider two supernova progenitor masses with homogeneous and clumpy ejecta to assess the chemical type and quantity of dust that forms. Grain size distributions are derived for all dust components as a function of post-explosion time.Methods. The chemistry of the gas phase and the simultaneous formation of dust clusters are described by a chemical network that includes all possible processes that are efficient at high gas temperatures and densities. The formation of key bimolecular species (e.g., CO, SiO) and dust clusters of silicates, alumina, silica, metal carbides, metal sulphides, pure metals, and amorphous carbon is considered. A set of stiff, coupled, ordinary, differential equations is solved for the gas conditions pertaining to supernova explosions. These master equations are coupled to a dust condensation formalism based on Brownian coagulation. Results. We find that Type II-P supernovae produce dust grains of various chemical compositions and size distributions as a function of post-explosion time. The grain size distributions gain in complexity with time, are slewed towards large grains, and differ from the usual Mathis, Rumpl, & Nordsieck power-law distribution characterising interstellar dust. Gas density enhancements in the form of ejecta clumps strongly affect the chemical composition of dust and the grain size distributions. Some dust type, such as forsterite and pure metallic grains, are highly dependent on clumpiness. Specifically, a clumpy ejecta produces large grains over 0.1 µm, and the final dust mass for the 19 M progenitor reaches 0.14 M . Clumps also favour the formation of specific molecules, such as CO 2 , in the oxygen-rich zones. Conversely, the carbon and alumina dust masses are primarily controlled by the mass yields of alumina and carbon in the ejecta zones where the dust is produced. The supernova progenitor mass and the 56 Ni mass also affect dust production. Our results highlight that dust synthesis in Type II-P supernovae is not a single and simple process, as often assumed. Several dust components form in the ejecta over time and the total dust mass gradually builds up over a time span around three to five years post-outburst. This gradual growth provides a possible explanation for the discrepancy between the small amounts of dust formed at early post-explosion times and the high dust masses derived from recent observations of supernova remnants.