  We review the effects of electron-electron interactions on the ground-state
spin and the transport properties of ultra-small chaotic metallic grains. Our
studies are based on an effective Hamiltonian that combines a superconducting
BCS-like term and a ferromagnetic Stoner-like term. Such terms originate in
pairing and spin exchange correlations, respectively. This description is valid
in the limit of a large dimensionless Thouless conductance. We present the
ground-state phase diagram in the fluctuation-dominated regime where the
single-particle mean level spacing is comparable to the bulk BCS pairing gap.
This phase diagram contains a regime in which pairing and spin exchange
correlations coexist in the ground-state wave function. We discuss the
calculation of the tunneling conductance for an almost-isolated grain in the
Coulomb-blockade regime, and present measurable signatures of the competition
between superconductivity and ferromagnetism in the mesoscopic fluctuations of
the conductance.
