  We use N-body/gasdynamical LambdaCDM cosmological simulations to examine the
effect of the assembly of a central galaxy on the shape and mass profile of its
dark halo. Two series of simulations are compared; one that follows only the
evolution of the dark matter component and a second one where a baryonic
component is added. These simulations include radiative cooling but neglect
star formation and feedback, leading most baryons to collect at the halo center
in a disk which is too small and too massive when compared with typical spiral.
This unrealistic model allows us, nevertheless, to gauge the maximum effect
that galaxies may have in transforming their dark halos. We find that the shape
of the halo becomes more axisymmetric: halos are transformed from triaxial into
essentially oblate systems, with well-aligned isopotential contours of roughly
constant flattening (c/a ~ 0.85). Halos always contract as a result of galaxy
assembly, but the effect is substantially less pronounced than predicted by the
"adiabatic contraction" hypothesis. The reduced contraction helps to reconcile
LambdaCDM halos with constraints on the dark matter content inside the solar
circle and should alleviate the long-standing difficulty of matching
simultaneously the scaling properties of galaxy disks and the luminosity
function. The halo contraction is also less pronounced than found in earlier
simulations, a disagreement that suggests that halo contraction is not solely a
function of the initial and final distribution of baryons. Not only how much
baryonic mass has been deposited at the center of a halo matters, but also the
mode of its deposition. It might prove impossible to predict the halo response
without a detailed understanding of a galaxy's assembly history. (Abriged)
