  We analytically investigate a new family of horizonless compact objects in
vector-tensor theories of gravity, called ultracompact vector stars. They are
sourced by a vector condensate, induced by a non-minimal coupling with gravity.
They can be as compact as black holes, thanks to their internal anisotropic
stress. In the spherically symmetric case their interior resembles an
isothermal sphere, with a singularity that can be resolved by tuning the
available integration constants. The star interior smoothly matches to an
exterior Schwarzschild geometry, with no need of extra energy-momentum tensor
at the star surface. We analyse the behaviour of geodesics within the star
interior, where stable circular orbits are allowed, as well as trajectories
crossing in both ways the star surface. We analytically study stationary
deformations of the vector field and of the geometry, which break spherical
symmetry, and whose features depend on the vector-tensor theory we consider. We
introduce and determine the vector magnetic susceptibility as a probe of the
star properties, and we analyze how the rate of rotation of the star is
affected by the vector charges.
