A detailed PAH growth model is developed, which is solved using a kinetic Monte-Carlo algorithm. The model describes the structure and growth of planar PAH molecules, and is referred to as the kinetic Monte-Carlo---aromatic-site (KMC-ARS) model. A PAH growth mechanism based on reactions at radical sites, which are available in the literature, is used to model the PAH growth processes. The motivation for this model is the development of a detailed soot particle population balance model which describes the evolution of an ensemble of soot particles based on their PAH structure. However, at present incorporating such a detailed model into a population balance is computationally unfeasible. Therefore, a simpler model referred to as the site-counting model has been developed, which neglects the relative structural information of PAHs in soot particles. The KMC-ARS model presented here is used to develop correlations and statistics which describe such PAH structural information in a simple, rapidly evaluated manner. These correlations and statistics are implemented in the site-counting model, and results of the site-counting model and the KMC-ARS model are compared. There is found to be reasonable agreement between the two models, therefore the site-counting model can be used with confidence in a soot particle population balance. Additionally the effect of steric hinderance in large PAH structures is investigated and correlations for site unavailable for reaction are presented.