We present a hydrodynamical simulation of an Antennae-like galaxy merger at parsec resolution, including a multicomponent model for stellar feedback and reaching numerical convergence in the global star formation rate for the first time. We analyse the properties of the dense stellar objects formed during the different stages of the interaction. Each galactic encounter triggers a starburst activity, but the varying physical conditions change the triggering mechanism of each starburst. During the first two pericentre passages, the starburst is spatially extended and forms many star clusters. However, the starburst associated with the third, final passage is more centrally concentrated: stars form almost exclusively in the galactic nucleus and no new star cluster is formed. The maximum mass of stars clusters in this merger is more than 30 times higher than those in a simulation of an isolated Milky Way-like galaxy. Antennae-like mergers are therefore a formation channel of young massive clusters possibly leading to globular clusters. Monitoring the evolution of a few clusters reveals the diversity of formation scenarios including the gathering and merger of gas clumps, the monolithic formation and the hierarchical formation in sub-structures inside a single cloud. Two stellar objects formed in the simulation yield the same properties as ultracompact dwarf galaxies. They share the same formation scenario than the most massive clusters, but have a larger radius either since birth, or get it after a violent interaction with the galactic centre. The diversity of environments across space and time in a galaxy merger can account for the diversity of the stellar objects formed, both in terms of mass and size.