Steam (zeiah) is a more interesting issue, in my opinion, for the steam of a liquid has the same status as the food from which it was derived. This has implications for not only cooking milk and meat dishes separately, but when cooking one after the other. Thus, the steam from a meat dish will rise up to the roof of the over and make it fleishig. Afterward, if one cooks an uncovered milk dish in the over, the steam will rise up, absorb the meat taste from the roof, and drip back into the milk dish. Uh oh, basar v'chalav - treif!!! So, if one does not have separate ovens for milk and meat, one should "designate" the oven for - say - meat, and ensure that when cooking milk the pot is always covered.
Obviously, this is an oversimplification, since there are issues like bitul, nosem taam lifgam, etc. Again, ask your LOR. (Or Rabbi Abadi, who says that there is no such thing as a "fleishig oven".)
But let's come back to a sentence which should have made you pause. The steam of a liquid has the same status as the food from which it was derived. If you just glossed over it, here is what it is saying: if one distills water from milk, the water is considered milchig. If one distills water from chicken soup, the water is considered fleishig. Now, for those who don't remember their elementary school science, distilled water contains nothing but water. Distilled water from milk is indistinguishable from distilled water from chicken soup, or from dog soup, or from industrial waste.
According to wiki, the knowledge of distillation was known in Mesopotamia at least back to the 2nd millenium BCE. So why don't the poskim (who rely on the Rosh who relies on a mishnah in Machshirim) seem to know about this??
Addendum! I should have done a search on this topic before posting it, but please also refer to this entry by Orthoprax, posted over three years ago.