Salamun Alaikum,
It is important to note that the division of the Quran into 'juz' (plural: ajza) / 'paras' (30) is different from the division of the Quran into surahs (Chapters - 114).
I do not concur that the division of the Quran into 30 paras were actioned under the supervision of the Prophet. There is no proof for this. However, we do have the Quran in its surah format which is attested by a mutawwatir recitation of the Quran and the earliest manuscripts.
The earliest manuscripts show no markings whatsoever to distinguish paras / juz. They only show divisions into surahs. The Quran clearly talks about the Quran being divided into parts but this has nothing to do with paras / ajza.
017.106"And (it is) a Qur'an that We have divided, that you may recite it to mankind at intervals, and We have revealed it by (successive) revelation" Many ajza (plural of juz) stop in-between surahs cutting the theme of the continuous dialogue. We are warned not to divide the Quran into parts in accordance to our will. This was a practice that started in some manner even at the time of the Prophet.
015.091-92 "(So also on such) as have made Qur'an into parts (as they please). Therefore, by your Lord, We will surely question them all about what they used to do"Therefore, I cannot concur with either of your propositions as correct. The Quran was fully transcribed in the life of the Prophet and it is my opinion that the surah format was also completed within the life of the Prophet. The division of the Quran into the juz / para format is a later invention.
Please see the following related article:
THE COMPILATION OF THE QURANhttp://quransmessage.com/articles/the%20compilation%20of%20the%20quran%20FM3.htm I hope that helps, God willing.
Regards.
Joseph.