An ultra low flow liquid distributor generates a very thin yet continuous liquid film over the entire width of a transfer surface. The ultra low flow liquid distributor includes a liquid supply system starting from a common main supply, which is split by repetitive bifurcations into a multitude of liquid sub-mains, until eventually each liquid supply sub-main feeds into one of the many liquid outlet openings. In this the liquid outlet openings are arranged above the liquid supply system, which automatically ensures self-priming.