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We prove that the minimally displaced set of a relatively irreducibleautomorphism of a free splitting, situated in a deformation space, is uniformlylocally finite. The minimally displaced set coincides with the train trackpoints for an irreducible automorphism.  We develop the theory in a general setting of deformation spaces of freeproducts, having in mind the study of the action of reducible automorphisms ofa free group on the simplicial bordification of Outer Space. For instance, areducible automorphism will have invariant free factors, act on thecorresponding stratum of the bordification, and in that deformation space itmay be irreducible (sometimes this is referred as relative irreducibility).

The minimally displaced set of an irreducible automorphism is locally finite