It struck me reading the Wikipedia article about The Twelve Caesars that there's no mention of the history of the book as a book between 121 AD when it was written and the 20th Century, at which point several translations and editions are given.
What actually happened to the book over the intervening years? If we did a census every century, would it turn up in say dozens of libraries, hundreds of libraries or thousands of libraries each time?
Do we have a good sense that it, e.g., was present first in Rome and then in Byzantium, and then in the Arab World, and then it was transmitted back to Western Europe? Or were there always some copies in Italy? Was it transmitted consistently in Latin or translated back and forth?
How old is the oldest extant copy of The Twelve Caesars? Do we have a general idea of how many "generations" of transcriptions there were between it and an original from 121 AD? How many extant copies are there that predate the invention of the printing press (if any)?
I've asked about The Twelve Caesars to keep the question as clear and specific as possible, but honestly I'm equally interested in any Ancient Roman book. I'd also be interested in what search terms I could use for further research (because it's a book of history, googling about its history as a book hasn't been very helpful!)
You picked a good example - Suetonius' Lives have an interesting history! His work was very popular for the rest of the Roman period - lots of other writers quoted from him directly (Eutropius, Aurelius Victor, Orosius), or used his biographies as a model for their own work. In the early third century, someone called Marius Maximus wrote a sequel to Suetonius, covering the emperors up to Elagabalus. These biographies don't survive but Ammianus Marcellinus (28.44.14) mentions them in the same breath as Suetonius so they must've been similar. The strange and complicated text known as the Historia Augusta, probably written at the end of the 4th century, is also modelled after Suetonius, but exactly what is going on with these things is anyone's guess. Paulinus' biography of St Ambrose (5th century) and even Einhard's Life of Charlemagne (9th century) clearly imitate Suetonius too. His work was present in the Byzantine empire too - John Lydus had a full copy of it in the 6th century, and the Suda, a huge encyclopedia written in the 10th century, lists the names of all Suetonius' works, most of which are now lost to us. There are some other fragmentary texts of Suetonius in Greek monasteries through to the 12th century.
At this point it's worth noting that even the 12 Caesars isn't complete as we have it. There must be some stuff missing from the beginning, including the dedication and the first chunk of Julius Caesar. As I said, Lydus had the whole thing in the 500s, but our oldest surviving manuscript, dating to AD 820 and coming from from Tours in France, is missing the beginning. From there, the surviving portions of the work were copied and recopied in monasteries across Western Europe - we have manuscripts from Germany, France and Italy from across the 11th, 12th and 13th centuries - until the first printed editions appear in the 15th.
Hope this helps! For your own googling purposes, the term you are looking for is 'manuscript tradition.'
Edit: wow, thanks for the Platinum award kind stranger!