The genetic analysis of composite data is very complicated, mainly because it is necessary to adjust data to the effects of heterosis and breed complementarity, and because there is usually considerable confounding of these data with several other effects, such as contemporary group effects, breed composition of the animal and maternal breed composition, among others. Data on birth weight (n = 151,083), weaning weight adjusted to 205 days (n = 137,257), yearling weight adjusted to 390 days (n = 61,410), weight gain from weaning to yearling (n = 56,653), and scrotum circumference (n = 23,323) and muscle score (n = 54,770), both adjusted to 390 days, from Bos taurus x Bos indicus composite beef calves born from 1994 to 2003 were analyzed to estimate (co)variance components and genetic parameters of growth traits. The animals belonged to the Montana Tropical program. Estimation was made by three models that approach adjustment to heterozygosis in order to suggest the best model. The RM model included contemporary groups, class of age of dam, outcrossing percentages for direct and maternal effects, and direct and maternal additive genetic breed effects as covariates; the R model was the same as RM, but without additive maternal breed effects, and H was the same as RM, but not considering any additive breed effect. Both R2 values and consistency of genetic parameters indicate that the more complex model (RM), which considers maternal and individual additive genetic breed effect, produces the best estimates when compared to other models. The R model seems to overestimate (co)variance components. The magnitudes of direct and maternal heritability estimates, obtained in this study, would permit genetic improvement for weight and growth traits, as much by selection of direct genetic effects for weight and growth as for the improvement of maternal performance, but in different lineages. Therefore, the correlations between these effects were unfavorable.