This is about the time of 1 Kings 16:30-33. Obviously this was before the full OT existed, but how many copies of the scrolls would have been in use? One in the Temple and.... how many elsewhere in old Israel-Judah, which other centres would have had them? Presumably only those places which had people able to read them and know their value.
The DSS are a later copy that ended up in the care of the Essenes, a celibate community near the Dead Sea. To my mind, this sounds like a disaster-recovery file set such as a modern corporation would keep of all its critical data on a hard drive somewhere distant from the company offices in case of fire. Alternatively, The DSS may have been the personal property of an individual who sought sanctuary with the Essenes (a group that had also renounced worldly goods). I'm thinking of an earlier time though, one where paper was expensive and few people could read or write unless they were from the elite who'd been trained. Kings had scribes to read stuff to them, so few bothered to learn. JC was from the poor, and so had no training. Matthew was a tax-collector, so had received the customary training when a boy. Priests had to be able to read the first scrolls reported to be carried in the Ark and known to have been present in the Temple archive at the time of Jeremiah (who seems to have been the author of Deuteronomy). My point is that the Bible as we know it was still under construction at this time, and in theory not much more than the first five books plus the books of Kings and Chronicles covering the history up to the time of Ahab and Jezebel would have existed - the remaining incidents and stories in the rest of the modern Bible had not yet happened. Old pictures of the Ark show it to have pigeon holes for a small number of scrolls, but what is not clear is how the scrolls were used. The Temple was not a place where a congregation was admitted and preached to; mass blessing of livestock for slaughter took place in the precincts outside and non-priests were not allowed into the inner sanctum even if they went to discuss religious matters with the priests in the Temple itself. Today, with a larger literate population, synagogues are the centres for dissemination of teachings, but at the time of Jeroboam, only the principle teaching centres of Jerusalem, Beth-El and Dan seem to have existed. If the priests kept their scrolls in each temple for safety, and it was not yet the custom for private individuals to have their own copies of the scrolls, my question is 'were there more than three sets of scrolls at the time of Jeroboam?' and if Ahab's father Omri had founded Samaria and built a palace there, did he build a temple as well? I assume that each place of worship would have had one set of scrolls, but how many centres were there really? Interpretation was a key skill, so it is unlikely that non-priests would have been allowed to have personal copies. This was also the state in pre-literate post-Roman England when the text was in Latin - only a few of the elite could read well enough to own lavishly illustrated bibles or prayer-books. By the time of Christ, the Torah was read by many of the devout elite, hence Nathaneal is found reading it under a fig tree, which was the custom of that period. A 'thin' Bible is easier to memorise and discuss, but how many actual copies would likely have existed in 850 BC? If it was more than four, where were they housed and who owned them?
Do you mean the dead sea scrolls?