About the Kwisatz haderach (spoilers probably)

So, as I understand it, the kwisatz haderach is the one who can be at many places at once, as well as the one who can look into the male genetic heritage (among other things).

I'm more interested in the "being at many places at once" ability. Is it just me or this part of the prophecy is never achieved nor mentioned in the story after Paul takes and transforms the water of life, making him the kwisatz haderach?

Not even Leto II can be at many places at once, he can just run very fast and he is supposed to be something even more that the kwisatz haderach (I can't remember what is it called).

So what happened to the "being at many places at once" part is really what i want to know? Did it simply got dropped from the story line, did F. Herbert forget about it, or is it somehow explained in the books?