Elfen Lied

The story involves human mutations called "Diclonius", who grow horns on their heads and possess telekinetic powers, in the form of invisible "arms" called vectors.
The tendency for violence among Diclonii varies among characters. Certain scientists contain them in a Facility in cells, where they are subject to inhumane experiments to test their abilities or where they await execution for being too dangerous.
An infectious virus is also associated with the mutation. This virus is spread through non-lethal contact with the vectors of a diclonius.
The main non-mutant character in the story is Kouta, who ends up becoming increasingly involved with these dicloniuses, as they seek refuge from the scientists.
The main diclonius character is Lucy/Nyuu, a killer whose alter ego is a hapless and very cute child whose vocabulary and intelligence are quite limited.