Context. The fragmentation of massive molecular clumps into smaller, potentially star-forming cores plays a key role in the processes of high-mass star formation. The ALMAGAL project, using the Atacama Large Millimeter/submillimeter Array (ALMA), offers highr-esolution data to investigate these processes across various evolutionary stages in the Galactic plane. Aims. This study aims at correlating the fragmentation properties of massive clumps, obtained from ALMA observations, with their global physical parameters (e.g., mass, surface density, and temperature) and evolutionary indicators (e.g., luminosity-to-mass ratio and bolometric temperature) obtained from Herschel observations. It seeks to assess whether the cores evolve in number and mass in tandem with their host clumps and to determine the possible factors influencing the formation of massive cores (M > 24 M⊙). Methods. We analyzed the masses of 6348 fragments, estimated from 1.4 mm continuum data for 1007 ALMAGAL clumps. Leveraging this unprecedentedly large dataset, we evaluated statistical relationships between clump parameters, estimated over ~0.1 pc scales, and fragment properties, corresponding to scales of a few thousand astronomical units, while accounting for potential biases related to distance and observational resolution. Our results were further compared with predictions from numerical simulations. Results. The fragmentation level correlates preferentially with clump surface density, supporting a scenario of density-driven fragmentation; however, it does not show any clear dependence on total clump mass. Both the mass of the most massive core and the core formation efficiency exhibit a broad range and increase, on average, by an order of magnitude across intervals defined by evolutionary indicators such as clump-dust temperature and the luminosity-to-mass ratio. This suggests that core growth continues throughout clump evolution, favoring clump-fed over core-fed theoretical scenarios. However, significant scatter in these relationships indicates that multiple factors, including magnetic fields, turbulence, and stellar feedback, not quantifiable with continuum data, influence fragmentation, as also suggested by comparison with numerical simulations.
