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For any stable curve $f$ in an exploded manifold, this paper constructs afamily of curves $\hat f$ with universal tropical structure which contains $f$.Such a family has the property that any other family of curves containing $f$is locally a small modification of a family which factors through $\hat f$. Assuch, families of curves with universal tropical structure play an importantrole in the analysis of the moduli stack of curves and the construction ofGromov-Witten invariants of exploded manifolds.

Universal tropical structures for curves in exploded manifolds