ABSTRACT We study the assembly of globular clusters (GCs) in 9 galaxy clusters using the cosmological simulation Illustris. GCs are tagged to individual galaxies at their infall time. The tidal removal of GCs from their galaxies and the distribution of the GCs within the cluster is later followed self-consistently by the simulation. The method relies on the simple assumption of a single power-law relation between halo mass (Mvir) and mass in GCs (MGC) as found in observations. We find that the GCs specific frequency SN as a function of V-band magnitude naturally reproduces the observed ‘U’-shape due to the combination of the power law MGC–Mvir relation and the non-linear stellar mass (M*)–halo mass relation from the simulation. Additional scatter in the SN values is traced back to galaxies with early infall times due to the evolution of the M*–Mvir relation with redshift. GCs that have been tidally removed from their galaxies form the present-day intracluster component, from which about $∼ \!60{{\ \rm per\ cent}}$ were brought in by galaxies that currently orbit within the cluster potential. The remaining ‘orphan’ GCs are contributed by satellite galaxies with a wide range of stellar masses that are fully tidally disrupted at z = 0. This intracluster component is a good dynamical tracer of the dark matter potential. As a consequence of the accreted nature of most intracluster GCs, their orbits are fairly radial with a predicted orbital anisotropy β ≥ 0.5. However, local tangential motions may appear as a consequence of localized substructure, providing a possible interpretation to the β < 0 values suggested in observations of M87.