  In this paper we study the four-point correlation function of the
energy-momentum supermultiplet in theories with N=4 superconformal symmetry in
four dimensions. We present a compact form of all component correlators as an
invariant of a particular abelian subalgebra of the N=4 superconformal algebra.
This invariant is unique up to a single function of the conformal cross-ratios
which is fixed by comparison with the correlation function of the lowest
half-BPS scalar operators. Our analysis is independent of the dynamics of a
specific theory, in particular it is valid in N=4 super Yang-Mills theory for
any value of the coupling constant. We discuss in great detail a subclass of
component correlators, which is a crucial ingredient for the recent study of
charge-flow correlations in conformal field theories. We compute the latter
explicitly and elucidate the origin of the interesting relations among
different types of flow correlations previously observed in arXiv:1309.1424.
