- There probably is not a specific term for this intersection of "musical role" and "rhythm".
- The nearest thing to what you describe would be analysis of style, or maybe directly analysis of rhythm itself.
Part 0: Terminological clarification
Now, the explanation must first start with a little correction in terminology. In polyphonic music, and even in homophonic music, terms such as "lead part" and "supporting part" are not the ones typically employed. In simple homophonic music, the ear will naturally tend towards the two extremes. Most frequently, the top voice is the "melody" (in a choral piece, this is also usually sung by the "soprano" section, so that's another term) while the lowest one is the "bass line" (or simply the "bass").
Where this gets more complex, and why I'm making a point out of this, is that in polyphony, there is no such clear cut distinction. The whole point of polyphony, in fact, is that there is usually no true "leading" or "supporting" voice, but that each part has something interesting of its own (in properly written homophony, each voice will also be "interesting", i.e. relatively melodic and singable, but they will usually not be that independent). Instead, using terminology borrowed from vocal music, each part will be designated by its approximate register, for ex. the top one will (unless you're specifically dealing with vocal polyphonic music written for a different grouping) be the "soprano", then "alto", "tenor", and the lowest one "bass" (of course, this can be extended in different ways if there are more than four voices in your polyphony). For ex., in the first fugue of Bach's Well Tempered Clavier, we have, in order, the alto, soprano, tenor and bass introducing the fugue's subject:
Part 1: There are no (broadly-speaking) standard rhythmic patterns
Moving on, rhythmic and melodic differences between voices in polyphonic music can range from basically none, say if voices are singing a simple piece in canon, ex. the 4th stanza (from 1 min. 27 sec) of this recording of a tune by Tallis, each voice starting one full measure after the other one...
...through to contrapuntal pieces based on augmentation and diminution (where each part has technically the same rhythm, but at a different pace, for ex. no. 3d of Bach's Musical Offering, BWV 1079)...
...all to way to a complex interplay of question and answer topped off with a fugue in the final part as in Bach's "Singet dem Herrn ein neues Lied", BWV 225 (audio with score; the whole piece is very interesting).
My examples so far are mostly vocal but of course this also holds for instrumental music. By the time Mozart and Haydn, when polyphony took a backstep, and the new genre en vogue was the piano sonata, the rhythms and melodic patterns did become somewhat more clearly hierarchised, for example the typical "Alberti bass", or the melody being rather freer than the accompaniment, ex. Haydn's Sonata in F major, Hob. XVI:23. Here again composers like showcasing their craft and creativity, and it's not uncommon to see a melodic fragment passed between the "melody" and the "accompaniment", or a motive which one has seen in the bass then appearing in the melody: ex. the first movement of Mozart's Sonata in A minor, K.310. In fact, it would be quite boring if there was no such variety: compositions would be very predictable... This also applies to romantic Lieder (where although the singer is very clearly the main thing, the accompaniment is by no means some static background). As you may have guessed, I could go on and on with examples (symphonies?, ...)
Part 2: What common patterns one can find are more properly attributed to style
The main point is that what rhythmic and melodic devices (and other tools used to organise musical speech) are most common depends a lot on the specific style and era, and the nature of the piece itself. After all, a piano sonata will not feature the same instrument-specific writing as a string quartet; and a choral piece by a composer such as Mendelssohn will not have so much in common with the contrapuntal writing of baroque motets or the word painting of late renaissance madrigals, even if all are written for the same instrument, i.e. the human voice.
Musicologists do study these differences within and without particular genres, but in a far wider scope than simply "what is the length of the notes usually used in each role". One can find plenty of specific references depending on the repertoire you're interested in, though of course I can neither read your thoughts nor guess what that would be for you.
Of course, if what you're looking for is literature specifically about rhythm and its role in music, mostly independently from other stylistic considerations, such documents are indeed quite plentiful, a good starting point if you have none would be the bibliographies provided in specialist encyclopedias such as Grove (art. "Rhythm") or the German-language MGG (art. "Rhythmus").
Hopefully, this at least provides further food for thought about the matter, if not the precise answer you're looking for.