  We present a detailed comparison of coalescence and thermal-statistical
models for the production of (anti-)(hyper-)nuclei in high-energy collisions.
For the first time, such a study is carried out as a function of the size of
the object relative to the size of the particle emitting source. Our study
reveals large differences between the two scenarios for the production of
objects with extended wave-functions. While both models give similar
predictions and show similar agreement with experimental data for
(anti-)deuterons and (anti-)3He nuclei, they largely differ in their
description of (anti-)hyper-triton production. We propose to address
experimentally the comparison of the production models by measuring the
coalescence parameter systematically for different (anti-)(hyper-)nuclei in
different collision systems and differentially in multiplicity. Such
measurements are feasible with the current and upgraded Large Hadron Collider
experiments. Our findings highlight the unique potential of ultra-relativistic
heavy-ion collisions as a laboratory to clarify the internal structure of
exotic QCD objects and can serve as a basis for more refined calculations in
the future.
