Abstract Depending on the stellar type, more than 15% of stars in the field have at least two stellar companions. Hierarchical triple systems can be assembled dynamically in dense star clusters, as a result of few-body encounters among stars and/or compact remnants in the cluster core. In this paper, we present the demographics of stellar and compact-object triples formed via binary–binary encounters in the CMC Cluster Catalog, a suite of cluster simulations with present-day properties representative of the globular clusters (GCs) observed in the Milky Way. We show how the initial properties of the host cluster set the typical orbital parameters and formation times of the formed triples. We find that a cluster typically assembles hundreds of triples with at least one black hole (BH) in the inner binary, while only clusters with sufficiently small virial radii are efficient in producing triples with no BHs. We show that a typical GC is expected to host tens of triples with at least one luminous component at present. We discuss how the Lidov–Kozai mechanism can drive the inner binary of these dynamically formed triples to high eccentricities, whenever it takes place before the triple is dynamically reprocessed by encountering another cluster member. Some of these systems can reach sufficiently large eccentricities to form a variety of transients and merger products, such as blue stragglers, X-ray binaries, Type Ia supernovae, Thorne–Zytkow objects, and gravitational wave sources.
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