  A measured solenoid is a laminated space endowed with a tranversal measure
invariant by holonomy, as defined in arXiv:0910.2836. A measured solenoid
immersed in a smooth manifold produces a closed current (known as generalized
Ruelle-Sullivan current). Uniquely ergodic solenoids are those for which there
is a unique (up to scalars) transversal measure. By the results in
arXiv:0910.2913, for any smooth manifold, any real homology class is
represented by a uniquely ergodic solenoid. In this paper, we prove that the
currents associated to uniquely ergodic solenoids are dense in the space of
closed currents, therefore proving the abundance of such objects.
