Supernova–driven outflows from early galaxies may have had a large impact on the kinetic and chemical properties of the intergalactic medium ( IGM ) . We use three–dimensional Monte Carlo cosmological realizations of a simple linear peaks model to track the time evolution of such metal–enriched outflows and their feedback on galaxy formation . We find that at most 30 % of the IGM by volume is enriched to values above 10 ^ { -3 } Z _ { \odot } in models that only include objects that cool by atomic transitions . The majority of enrichment occurs relatively early ( 5 \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } z \lower 2.15 pt \hbox { $ % \buildrel < \over { \sim } $ } 12 ) and leads to a mass-averaged cosmological metallicity between 10 ^ { -3 } Z _ { \odot } and 10 ^ { -1.5 } Z _ { \odot } . The inclusion of Population III objects that cool through { H } _ { 2 } line emission has only a minor impact on these results : increasing the mean metallicity and filling factor by at most a factor of 1.4 , and moving the dawn of the enrichment epoch to z \approx 14 at the earliest . Thus enrichment by outflowing galaxies is likely to have been incomplete and inhomogeneous , biased to the areas near the starbursting galaxies themselves . Models with a 10 \% star formation efficiency can satisfactorily reproduce the nearly constant ( 2 \leq z \leq 5 , Z \approx 3.5 \times 10 ^ { -4 } Z _ { \odot } ) metallicity of the low column density Ly \alpha forest derived by Songaila ( 2001 ) , an effect of the decreasing efficiency of metal loss from larger galaxies . Finally , we show that IGM enrichment is intimately tied to the ram-pressure stripping of baryons from neighboring perturbations . This results in the suppression of at least 20 % of the dwarf galaxies in the mass range \sim 3 \times 10 ^ { 8 } -3 \times 10 ^ { 9 } M _ { \odot } in all models with filling factors greater than 2 % , and an overall suppression of \sim 50 \% of dwarf galaxies in the most observationally-favored model .