The growth of out-of-equilibrium interfaces via computer simulation is of high relevance for investigating microscopic phenomena, for example, the role of atom diffusion in terraces and cluster perimeters. In addition, finding a set of scaling exponents allows us to classify interfaces within a universality class. If a normal surface roughness scale is observed, determining the global roughness exponent is equivalent to finding the local roughness exponent. Some results reported in the literature, obtained using computer simulations on models that are said to belong to the Villain-Lai-Das Sarma class (VLDS), suggest that the global roughness exponent is distinct from the local roughness exponent, which may lead to conclusions on which asymptotic anomalous scale exists in the VLDS class. Such feature may be justified by the global roughness exponents larger than the unit. In this thesis, we introduce a method for measuring local height fluctuations in interface, based on calculating the shortest distance from a profile point to a polynomial of degree adjustment n. The method is named the Optimal Fluctuations Analysis. (ODFAn ). We make a comparison with the method based on Detrended Fluctuations Analysis (DFAn ) and the standard local roughness method (DFA 0 ). The goal is to extract the local roughness exponent about profiles/surfaces generated by network models deposition, namely: Growth in a Restricted Solid-on-Solid model (CRSOS), (Das Sarma and Tamborenea-DT) and (Clarke Vvedensky-CV), believed to belong the VLDS class. We observe that these models present a transient regime in which profiles/surfaces have characteristic length (hill structures). For estimate the average lateral length of the hills, the value of the first zero or minimum of the normalized height-height auto-correlation function was used. Our results for the local roughness exponent extracted with the ODFA n method are compatible with the calculated exponent, using the group renormalization theory with first and second loop corrections for the VLDS class. For the CRSOS and DT models, the latter considering a situation where the noise reduction technique is applied in d = 1 dimensions and for the CV model, with d = 1.2 dimensions, we will use a polynomial adjustment with n = 1.2. A better scaling is observed for n = 2, where the effective local roughness exponents were extracted to scale lengths of the same order as the average lateral length of the hills. In the CV model at d = 2, an anomalous scale transient was investigated for small scales, calculating local roughness. Because it is a more realistic model for thin film growth simulation, we also study the distribution of the average number of steps, Np , of surface adsorbed atoms with the CV model, as a function of the parameters R and ε, where R is the ratio between the diffusion rate, D0 (considering atoms without side neighbors) is the deposition rate F, and ε is the parameter associated with the probability of detachment of atoms with their lateral neighbors. Our results show distributions in the form of extended exponentials under the low temperature regime. In the high temperature regime our results indicate that the average number of steps scales with Rε² , suggesting that when detachment from kink sites becomes possible, there is a large amount of displacement of atoms that control Np.