question: The analysis of correlation structures among multivariate spatially aggregated data has become increasingly important and poses substantial challenges This article concerns the development of partial and semi-partial statistics of spatial associations in the context of multivariate spatial areal data extending Moran's I and Geary's C The proposed statistical tools describe global or local associations among spatially aggregated measurements for pairs of different components conditional on all remaining components The new statistics are tested through a simulation study and illustrated using aggregated data on the COVID-19 pandemic recorded at the Community level in Spain © 2020 The Ohio State University