The custodian of the priceless gifts is the Monastery of St. Paul, one of twenty monasteries on the Mount Athos peninsula. Source: http://orthodoxwiki.org/St._Paul’s_Monastery_%28Athos%29
They were given to the Monastery by the widow of a sultan.
In the first century Mary gave them to the Jerusalem Church. They were located there until the year 400. Later, the Byzantine Emperor Arcardius translated them to Constantinople and placed them in the Hagia Sophia church. In 1453, Constantinople fell. In 1470 the daughter of the Serbian ruler George Brankovich, Maria (Maro), who was the widow of the Turkish sultan Murat (Murada) II (1404–1451), gave the Gifts of the Magi to the Monastery of St. Paul, which was Serbian until 1744. Despite the fact that she was the wife of a sultan she did not accept Islam and remained a Christian until the end of her life. Source: Fr. Andreas Blom https://andreasblom.wordpress.com/2012/01/11/what-happened-to-the-gifts-of-the-magi/
The gold is in the form of 28 pieces of carefully engraved coins of different shapes. Each coin has a different design of different and complex artistry. The frankincense and myrrh take the form of mixtures in the form of 62 roughly spherical beads the size of a small olive.