We report on the investigation of height distributions (HDs) and spatial covariances of two-dimensional surfaces obtained from extensive numerical simulations of the celebrated Clarke-Vvedensky (CV) model for homoepitaxial thin film growth. In this model, the effect of temperature, deposition flux, and strengths of atom-atom interactions are encoded in two parameters: the diffusion to deposition ratio $R=D/F$ and $varepsilon$, which is related to the probability of an adatom breaking a lateral bond. We demonstrate that the HDs present a strong dependence on both $R$ and $varepsilon$, and even after the deposition of $10^5$ monolayers (MLs) they are still far from the asymptotics in some cases. For instance, the temporal evolution of the HDs skewness (kurtosis) displays a pronounced minimum (maximum), for small $R$ and $varepsilon$, and only at long times it passes to increase (decrease) toward its asymptotic value. However, it is hard to determine whether they converge to a single value or different nonuniversal ones. For large $R$ and/or $varepsilon$, on the other hand, these quantities clearly converge to the values expected for the Villain-Lai-Das Sarma (VLDS) universality class. A similar behavior is observed in the spatial covariances, but with weaker finite-time effects, so that rescaled curves of them collapse quite well with the one for the VLDS class at long times. Simulations of a model with limited mobility of particles, which captures some essential features of the CV model in the limit of irreversible aggregation ($varepsilon=0$), reveal a similar scenario. Overall, these results point out that the study of fluctuations in homoepitaxial thin films surfaces can be a very difficult task and shall be performed very carefully, once typical experimental films have $lesssim 10^4$ MLs, so that their HDs and covariances can be in the realm of transient regimes.
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