  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.
