We study random dense packings of Heisenberg dipoles by numerical simulation. The dipoles are at the centers of identical spheres that occupy fixed random positions in space and fill a fraction $Phi$ of the spatial volume. The parameter $Phi$ ranges from rather low values, typical of amorphous ensembles, to the maximum $Phi$=0.64 that occurs in the random-close-packed limit. We assume that the dipoles can freely rotate and have no local anisotropies. As well as the usual thermodynamical variables, the physics of such systems depends on $Phi$. Concretely, we explore the magnetic ordering of these systems in order to depict the phase diagram in the temperature-$Phi$ plane. For $Phi gtrsim0.49$ we find quasi-long-range ferromagnetic order coexisting with strong long-range spin-glass order. For $Phi lesssim0.49$ the ferromagnetic order disappears giving way to a spin-glass phase similar to the ones found for Ising dipolar systems with strong frozen disorder.
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