Many people assert the Qur'an could not have been committed to paper during the time of the Prophet (peace and blessings be upon him), as paper was non-existent in Arabia at the time and that research has shown the Qur'an was written in different bits and pieces on wood and animal hyde.

Here are two non-Islamic sources that virtually prove the above assertions to be incorrect:

http://www.answers.com/topic/muhammad

According to the source above (which is in turn supported by several academic citations), the Prophet was born in the year 570 and began receiving divine revelation at the age of 40 (610).

According to the information from: http://www.paperonline.org/history/610/610_frame.html

"Chinese papermaking techniques reached Korea at an early date and were introduced to Japan in the year 610."
.......
"Very soon, knowledge of papermaking spread to Central Asia and Tibet and then on to India. When the Arabs, in the course of their eastern expansion, neared Samarkan they too became acquainted with the production of paper and paper mills were subsequently set up in Baghdad, Damascus and Cairo, and later in Morocco, Spain and Sicily. Owing to the lack of fresh fibres, the raw material used by the Arabs was made almost entirely from rags: however, their defective and poorly designed processing equipment (such as breaker mills) produced a rather inferior ground pulp. But, by using this method, with screens made of reeds, thin sheets were made and then ‘coated’ with starch paste. This gave Arabian paper its good writing properties and fine appearance."

More research still needs to be done on when the Arabs had access to paper, to confirm this idea, but it still casts serious doubt on the claims by some that they Qur'an could not have been written at the time.

The significance of this is that if papermaking techniques from China reached Korea and Japan by the year 610, where the Prophet began receiving revelation, certainly Chinese paper itself, along with the techniques must have been received soon or even before that time.

Even if someone can argue that the paper making techniques in Baghdad were not very advanced, it would have still been enough to write the Qur'an down on, and even failing that, certainly through the Silk Road the Arabs must have had paper available to them from China itself.

I believe this puts the claims by some that the Qur'an could not have been committed to paper during his time to rest.
One more claim, is that based on this information it is surprising why no one casts more doubt on the previous books (which we believe in) but were never written on paper since during the time of the Bible and Tor'ah it did not exist.