Why do people complicate this lol. I move from home and university 1-2 times a year talking 16 hours flights here, 1-2 days travelling. Nevertheless heres what I do. Motherboard, gpu, RAM, HDD as carry on in antistatic bags along with mouse and keyboard. Power supply into check in luggage, monitor too (i'm crazy like that) pack to shield it from damage. Imagine the forces it'd experience under 20 bags or being tossed, baggage handling is not gentle. ONCE AGAIN WRAP IT UP GOOD IN TOWELS, SWEATERS ETC IN THE CENTRE OF BAG WITH LOTS OF CUSHIONING.
Carry on bag has a few t-shirts, sweater etc used to cushion components. When you get to security tell them there and then you have a disassembled desktop in your carry on, remove each component and put them in a tray as you would laptops (if not they'll swab everything and stop to ask you more questions wasting your time. Also try and ignore the crazy stares people will give you). They may swab the components but thats ok, discharge static on the nice metal tables, repack and be on your merry way.
Never paid duty/tax as stuff looks used done this about 7 times now. Nothing broken/damaged yet. Maybe i'm just lucky 😛