We use N-body/gasdynamical cosmological simulations to examine the effect of the assembly of a central galaxy on the shape and mass profile of its surrounding dark matter halo . Two series of simulations are compared ; one that follows only the evolution of the dark matter component of individual halos in the proper \Lambda CDM cosmological context , and a second series where a baryonic component is added and followed hydrodynamically . The gasdynamical simulations include radiative cooling but neglect the formation of stars and their feedback . The efficient , unimpeded cooling that results leads most baryons to collect at the halo center in a centrifugally-supported disk which , due to angular momentum losses , is too small and too massive when compared with typical spiral galaxies . This admittedly unrealistic model allows us , nevertheless , to gauge the maximum effect that galaxies may have in transforming their surrounding dark halos . We find , in agreement with earlier work , that the shape of the halo becomes more axisymmetric : post galaxy assembly , halos are transformed from triaxial into essentially oblate systems , with well-aligned isopotential contours of roughly constant flattening ( \langle c / a \rangle \sim 0.85 ) . Halos always contract as a result of galaxy assembly , but the effect is substantially less pronounced than predicted by the traditional “ adiabatic contraction ” hypothesis . The reduced contraction helps to reconcile \Lambda CDM 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 galaxy luminosity function . The halo contraction we report 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 to galaxy formation without a detailed understanding of a galaxy ’ s detailed assembly history .