Envisioned chronology of the formation of trans-Neptunian objects. I. Formation. An initial burst of planetesimal formation populates bodies in the primordial belt (PB) at ~20 au and the cold classicals at ~40–50 au). It is assumed that the shape of the cold classicals and the primordial belt size distributions are similar, both featuring a tapered exponential at high mass. II. Growth: Pebble accretion, acting preferentially on the massive bodies, alters the size distribution of the PB. Growth takes place in a gas-rich medium. This is the phase investigated in this work. III. Implantation. Neptune’s migration disperses the PB with a implantation fraction f_impl,P48 populating the dynamically hot bodies within 48 au (population P48).