  We have analyzed a single vortex at T=0 in a 3D superfluid atomic Fermi gas
across a Feshbach resonance. On the BCS side, the order parameter varies on two
scales: $k_{F}^{-1}$ and the coherence length $\xi$, while only variation on
the scale of $\xi$ is seen away from the BCS limit. The circulating current has
a peak value $j_{max}$ which is a non-monotonic function of $1/k_F a_s$
implying a maximum critical velocity $\sim v_F$ at unitarity. The number of
fermionic bound states in the core decreases as we move from the BCS to BEC
regime. Remarkably, a bound state branch persists even on the BEC side
reflecting the composite nature of bosonic molecules.
