  We investigate the centrality-dependent validity of the
limiting-fragmentation hypothesis in relativistic heavy-ion collisions at
energies reached at the Relativistic Heavy Ion Collider (RHIC) and the Large
Hadron Collider (LHC). A phenomenological analysis of Au-Au and Pb-Pb
collisions within a three-source relativistic diffusion model (RDM) is
performed at sqrt(s_NN) = 19.6, 62.4, 130, 200, 2760 and 5023 GeV using four
centrality cuts at each energy. Linear and nonlinear expressions for the
rapidity drift function are tested and their physical relevance is discussed.
Our results are compatible with the limiting-fragmentation conjecture for the
investigated centralities in the full energy range. The number of particles in
the fragmentation and fireball sources are found to depend on sqrt(s_NN)
logarithmically and cubic-logarithmically, respectively.
