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Let $A$ and $B$ be two abelian groups. The group $A$ is called $B$-small if the covariant functor $\mathrm{Hom}(A,-)$ commutes with all direct sums $B^{\left(\kappa \right)}$ and $A$ is self-small provided it is $A$-small. The paper characterizes self-small products applying developed closure properties of the classes of relatively small groups. As a consequence, self-small products of finitely generated abelian groups are described.