Pulsed laser deposition is widely used to synthesize complex oxide thin films with advanced functional properties because of the versatility of the process, although the actual processes and mechanisms that take place are highly dynamic and nontrivial. Detailed understanding of the plume dynamics is required to achieve enhanced control of the growth of complex oxide thin films. However, analytical models of the plasma plume proposed in previous studies, the so-called shockwave model, drag model, and adiabatic thermalization model, only apply to a specific pressure regime and only focus on the propagation of the plasma front. Numerical modeling of the plasma dynamics has previously been pursued for the one-dimensional propagation of a Si plasma plume in a noble background gas. Here we have explored a more generalized numerical model for the dynamics of a TiO2 plasma plume by extending to three dimensions, multiple elements in the plasma plume, and including chemical reactions in an oxygen environment without the use of adaptive parameters, other than used for the description of the initial plume shape. Comparison between the simulations and the self-emission measurements of the TiO2 plasma plume shows good agreement. Our model enables detailed simulation of the oxidation state of the arriving particles (Ti, TiO, and TiO2) on the substrate surface depending on oxygen background pressure. Interestingly, low pressures of about 0.02 mbar result in fast oxygen particles arriving prior to the slower titanium particles, which could significantly influence the oxidation state of the initial substrate surface. The enhanced number of collisions for higher pressures of about 0.1 mbar leads to a large amount of the low-mass oxygen particles coming to a standstill 1-2 cm away from the ablated target. Furthermore, the three-dimensional nature of our model has enabled simulation of the lateral variations in composition of the deposited particles on the substrate surface. Although negligible variations in the Ti:TiO and Ti:TiO2 ratios are present for high pressures over deposition areas with diameters up to 5 cm, significant variations can be observed for low pressures. These insights could play an important role in upscaling pulsed laser deposition from a scientific laboratory-based scale to an industrial large-area scale.