Looking for a verb that means division into multiple branches
There's the simple intransitive multi-word verb fan out.
- The graphs fanned out beyond x = 1·6
fan out (from some place)
to spread outward from a particular area.
- The paths seem to fan out from the wide trail that starts at the house.
[McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002]
Diverge is perhaps a little more formal, but does not really generate the same image.
A few have felt the need to introduce 'polyfurcate', but thankfully dictionaries have ignored this.
One option would be the word fork
a division into branches or the place where something divides into branches
This can also be used as a verb, so you could say
Over half the range all curves are identical, but starting from 0, each curve forks.