The need to establish actual particle size distributions (PSDs) of soot emissions from the nanoscale upwards, along with the current global indicators based on soot mass, stems from increasingly strict regulatory demands. In the current work, a mass and number density preserving sectional model is coupled with a transported probability density function (PDF) method to study the evolution of soot PSDs in two non-premixed turbulent jet flames at Reynolds numbers of 10,000 and 20,000. The transported PDF approach is closed at joint-scalar level and includes mass fractions of gas phase species, soot sections, as well as enthalpy, leading to a fully coupled 78-dimensional joint-scalar space, treating interactions between turbulence and gas phase/soot chemistry as well as radiation without further approximation. The gas phase chemistry features 144 reactions, 15 solved and 14 steady-state species and an acetylene-based soot inception model is calibrated using comprehensive detailed chemistry up to pyrene and applied to a well-stirred/plug flow reactor configuration. The derived nucleation rate is subsequently applied in the turbulent flame calculations. Soot surface growth is treated via a PAH analogy and oxidation via O, OH and O2 is accounted for. The sectional model features 62 sections covering particle sizes in the range 0.38 nm  ≤ dp ≤ 4.4 µm and includes a model for the collision efficiency of small particles ( ≤ 10 nm) based on the Lennard–Jones potential. The computed results reproduce the evolution of the PSDs with encouraging accuracy. It is also shown that the distribution of soot in mixture fraction space is affected by local extinction events.