The current work studies the modelling of soot in turbulent combustion via a sectional model, a two-equation type approach, and the method of moments with interpolative closure in the framework of a transported probability density function model closed at joint-scalar level. Detailed sectional model calculations in a premixed well-stirred/plug flow reactor system are carried out, and updates to nucleation rates for acetylene-based soot nucleation models and soot oxidation rates used in previous work are proposed and evaluated. The updates are integrated into two-equation and method of moments calculations of two turbulent non-premixed jet flames burning ethylene and a methane based fuel, and the sensitivity to the surface area dependance of soot growth and oxidation is evaluated. Further, soot volume fraction statistics and particle size distributions (PSDs) were calculated for the turbulent ethylene flame using the sectional soot model, and an improved agreement with experimental data over the two-equation model results was noted, while the calculated PSDs demonstrate the capabilities of the model. Overall, the current work presents a significant advance upon previously published results obtained using a wide range of alternative approaches.