ant (last panel of Fig. \[fig:haloradflux\]). A mass flux that is independent of radius implies efficient mass transport, as the same amount of mass passes through each shell per unit of time. The inflowing mass flux decreases from 10$R_\mathrm{vir}$ to $\sim R_\mathrm{vir}$ because the overdensity of the region is increasing and because some of the gas that is infalling at distances $\gg R_{\mathrm{vir}}$ is falling towards neighbouring haloes. At $R\gtrsim R_\mathrm{vir}$ the outflowing mass flux decreases somewhat, indicating that the transportation of outflowing material slows down and that the galactic winds are becoming less efficient. This can also be seen by the drop in outflow fraction around the virial radius in the last panel of Fig. \[fig:haloradflux\]. (The small decrease in outflow fraction below $10^{10.5}$ M$_\odot$ is a resolution effect.) The outflowing mass flux increases again at large radii, because the hot-mode gas is falling towards unrelated haloes.

Comparing Figs. \[fig:halomassz2\] and \[fig:halomassflux\], we see again that, to first order, inflowing and outflowing gas behave similarly as cold-mode and hot-mode gas, respectively. There are, however, some clear differences, although we do need to keep in mind that some are due to the fact that Fig. \[fig:halomassz2\] is mass-weighted while Fig. \[fig:halomassflux\] is mass flux-weighted. The mass flux-weighted median temperature of outflowing gas is always close to the virial temperature. For $M_\mathrm{halo}\la 10^{11}$ M$_\odot$ this is much lower than the median temperature of hot-mode gas, but that merely reflects the fact that for these haloes the virial temperature is lower than the value of $10^{5.5}~$K that we use to separate the cold and hot modes. The mass flux-weighted maximum past temperature is about 0.5 dex higher than $T_\mathrm{vir}$.

Another clear difference is visible at the high-mass end ($M_\mathrm{halo}\ga 10^{12.5}$ M$_\odot$). While the cold-mode density increases rapidly with mass, the overdensity of i