The main objective of this study is to propose different probabilistic models for adjusting the trend component, since it significantly influences the quality of the spatio-temporal interpolation of rainfalls. We used the monthly total precipitation data of the São Francisco River Basin (SFRB) for the period of 31 years, 1989-2019. The SFRB occupies 8% of the whole Brazilian territory, mostly located in the Northeast Brazilian region. For the trend component, we propose the fitted GAMLSS models by comparing different probability distribution families, which in most cases include the characteristics of these data. The results indicate the existence of a spatio-temporal pattern of the residues obtained from the adjustment of the trend with zero adjusted Gamma distribution for the accumulated monthly precipitation. The adjustment revealed a spatial dependence of up to 873 km between the pluviometric stations and temporal autocorrelation of approximately 1.6 months. The methodology used in this study enabled us to create rainfall maps, interpolating unobserved locations in differences years. The projection of these maps to the SFRB is considered extremely important for planning and implementing activities related to water resources across the river basin.