  We report a systematic investigation, together with a theoretical analysis,
of the resistivity and Hall effect in single crystals of
Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$, over a wide doping range. We find a
surprisingly great disparity between the relaxation rates of the holes and the
electrons, in excess of an order of magnitude in the low-doping,
low-temperature regime. The ratio of the electron to hole mobilities diminishes
with temperature and doping (away from the magnetically ordered state) and
becomes more conventional. We also find a straightforward explanation of the
large asymmetry (compared to cuprates) of the superconducting dome: in the
underdoped regime the decisive factor is the competition between AF and
superconductivity (SC), while in the overdoped regime the main role is played
by degradation of the nesting that weakens the pairing interaction. Our results
indicate that spin-fluctuations due to interband electron-hole scattering play
a crucial role not only in the superconducting pairing, but also in the normal
transport.
