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Try contacting Xperia care who may have more detailed information regarding questions of this nature http://www.sonymobile.com/global-en/support/contact-us/
The Z2 works with Fat32 and exFAT drives (read/write).
Desktop drives 4tb work fine. If they're formatted exFAT then large files >4gb are supported.
Some bus powered drives (portable HDDs) pull too much current for the phone. A powered USB hub may be required.
Some users have reported inconsistent results with similar hard drives. This is almost certainly due to variations in the components used.