The unsteady two-dimensional conditional moment closure (CMC) model with first-order closure of the chemistry and supplied with standard models for the conditional convection and turbulent diffusion terms has been interfaced with a commercial engine CFD code and analyzed with two numerical methods, an “exact” calculation with the method of lines and a faster fractional-step method. The aim was to examine the sensitivity of the predictions to the operator splitting errors and to identify the extent to which spatial transport terms are important for spray autoignition problems. Despite the underlying simplifications, solution of the full CMC equations allows a single model to be used for the autoignition, flame propagation (“premixed mode”), and diffusion flame mode of diesel combustion, which makes CMC a good candidate model for practical engine calculations. It was found that (i) the conditional averages have significant spatial gradients before ignition and during the premixed mode and (ii) that the inclusion of physical-space transport affects the calculation of the autoignition delay time, both of which suggest that volume-averaged CMC approaches may be inappropriate for diesel-like problems. A balance of terms in the CMC equation before and after autoignition shows the relative magnitude of spatial transport and allows conjectures on the structure of the premixed phase of diesel combustion. Very good agreement with available experimental data is found concerning ignition delays and the effect of background air turbulence on them.