Prophet Muhammad (SAW) did not hand-over the Glorious Qur'an to his companions in an arranged form and in a single written volume because

A.

he did not want only the Quraish to inherit the book

B.

the revelation did not come in one piece but at intervals

C.

many tribes would want to take over its distribution

D.

there was no need for it

Correct answer is B

The prophet Muhammad (pbuh) was illiterate so whenever he received revelation of the Quran one of the scribes would write the verses down on materials like parchment, animal skin, leather, bones and stone tablets. The Prophet (pbuh) would check that the verses had been written correctly by asking the scribe to recite the verses back to him. Some of his scribes were: Abu Bakr-as-Siddeeq, Uthman ibn Affan, Ali ib Abi Talib, Abu Salama, Zayd ibn Thabit etc.
By the time the Prophet Muhammad (pbuh) passed away in 632 CE the complete Quran had been written down on various materials. The Quranic fragments were then used to prepare a complete master copy of the Quran during the Caliphate of Uthman ibn Affan. Zayd ibn Thabit was instructed to compile a master copy of the Quran from all the loose material. Muhammad (pbuh) had read the Quran in a certain order which was memorised by many people during his life. Zayd requested every companion of the Prophet (pbuh) to bring him their written verses of the Quran. He only accepted written material which had been dictated by the Prophet (pbuh) himself.