  The key ingredient of the approach, presented in this paper, is the
factorization property of $SU(2)$ coherent states upon splitting or decay of a
quantum spin system. In this picture, the even and odd spin coherent states are
viewed as comprising two, three or more spin subsystems. From this perspective,
we investigate the multipartite quantum correlations defined as the sum of the
correlations of all possible bi-partitions. The pairwise quantum correlations
are quantified by entanglement of formation and quantum discord. A special
attention is devoted to tripartite splitting schemes. We explicitly derive the
sum of entanglement of formation for all possible bi-partitions. It coincides
with the sum of all possible pairwise quantum discord. The conservation
relation between the distribution of entanglement of formation and quantum
discord, in the tripartite splitting scheme, is discussed. We show that the
entanglement of formation and quantum discord possess the monogamy property for
even spin coherent states, contrarily to odd ones which violate the monogamy
relation when the the overlap of the coherent states approaches the unity.
