The First Master Copy
The word Quran means recitation, so the first "master copy" would be the hearts of millions of Muslims who know the Quran by heart. The people who know the entire Quran by heart are called as "Hafiz".
If you go to any hafiz from Malaysia to Mexico, you will see that they recite the same Quran. This is the same for any sect or denomination in Muslims.
When the Prophet (pbuh) received revelation, he would himself learn it by heart & teach his companions. He would later keep checking them to make sure all of them knew it properly.
Also, every Ramadhan most Mosque have a full Quran recitation to make sure those that who know the full Quran by heart get a revision, while those listening too get a revision of parts that they know. These prayers are called as "taraweeh".
The Next Master Copy
The oldest entire Quran is the official copy compiled by the companions of the Prophet (pbuh) under the third Khilafah Uthman. This was completed 19 years after the Prophet (pbuh) passed away.
They were the first generation who learnt the entire Quran from the Prophet (pbuh). This Quran is still present in Topkapı Palace, in Turkey
The Other Master Copies
If you go thru the ages, Muslims built many monuments. They had parts of the Quran etched on them. Those monuments have the same Quran that you will see people recite or in the copies we read at home.
1) Taj Mahal in Agra, India has the parts of the Quran etched on it.
2) Raudat Tahera in Mumbai, India has the full Quran etched on it.