We use high-resolution cosmological zoom-in simulations from the FIRE project to make predictions for the covering fractions of neutral hydrogen around galaxies at z=2-4. These simulations resolve the interstellar medium of galaxies and explicitly implement a comprehensive set of stellar feedback mechanisms. Our simulation sample consists of 16 main halos covering the mass range M_h~10^9-6x10^12 Msun at z=2, including 12 halos in the mass range M_h~10^11-10^12 Msun corresponding to Lyman break galaxies (LBGs). We process our simulations with a ray tracing method to compute the ionization state of the gas. Galactic winds increase the HI covering fractions in galaxy halos by direct ejection of cool gas from galaxies and through interactions with gas inflowing from the intergalactic medium. Our simulations predict HI covering fractions for Lyman limit systems (LLSs) consistent with measurements around z~2-2.5 LBGs; these covering fractions are a factor ~2 higher than our previous calculations without galactic winds. The fractions of HI absorbers arising in inflows and in outflows are on average ~50% but exhibit significant time variability, ranging from ~10% to ~90%. For our most massive halos, we find a factor ~3 deficit in the LLS covering fraction relative to what is measured around quasars at z~2, suggesting that the presence of a quasar may affect the properties of halo gas on ~100 kpc scales. The predicted covering fractions, which decrease with time, peak at M_h~10^11-10^12 Msun, near the peak of the star formation efficiency in dark matter halos. In our simulations, star formation and galactic outflows are highly time dependent; HI covering fractions are also time variable but less so because they represent averages over large areas.
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