The word ветвление (branching, ramification) appears to be a purely technical synonym for разветвление. I can find разветвление in ordinary dictionaries, but ветвление is not there, although it is mentioned in references on biology, chemistry, computer programming, and mathematics.
Is ветвление restricted to usage in the natural sciences and math, and can someone explain why the adjectival form разветвлённый is used but ветвлённый apparently doesn't exist?
Ветвление is always a process, whereas разветвление can be either a process or the physical place where something is branching out, the actual "fork". Ветвлённый doesn't exist because ветвиться is not a transitive verb - it doesn't have a оbject, just the subject. It's like краснеть (to blush), for example. You can't blush something, you can only blush yourself.
So, the outcome of ветвление will be an object that is ветвистый or разветвлённый itself. A "ветвлённый" object would be something that ветвление was done to it, like варёный.
Your question is about participles ("ветвлённый", "разветвлённый") and nouns ("ветвление", "разветвление"). In this case both seem to originate from the corresponding verbs ("ветвиться", "разветвляться").
The difference between the two verbs is that one "ветвиться" is in imperfective aspect and "разветвляться" is in perfective aspect.
Accordingly, the word "разветвление" can refer to some simple things like a branch of a railroad, and "ветвление" describes some sort of a phenomenon in general. That naturally restricts the usage of the word to scientific context.
As for "ветвлённый", I Vitaly's answer, that's just popped up as I'm typing mine, covers it better than I could have.
