  The zero temperature value of the in-plane London penetration depth,
$\lambda_{ab}(0)$, has been measured in single crystals of
Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ as a function of the Co concentration, $x$,
across both the underdoped and overdoped superconducting regions of the phase
diagram. For $x\gtrsim0.047$, $\lambda_{ab}(0)$ has been found to have values
between 120 $\pm$ 50~nm and 300 $\pm$ 50~nm. A pronounced increase in
$\lambda_{ab}(0)$, to a value as high as 950 $\pm$ 50~nm, has been observed for
$x\lesssim0.047$, corresponding to the region of the phase diagram where the
itinerant antiferromagnetic and superconducting phases coexist and compete.
Direct determination of the doping-dependent $\lambda_{ab}(0)$ has allowed us
to track the evolution of the temperature-dependent superfluid density, from
which we infer the development of a pronounced superconducting gap anisotropy
at the edges of the superconducting dome.
