RIP Union Carrier, we've got some clunkier combos that still work without him.
Ash-proof combo:
Pieces - 1 Hangar + 1 A/B/C OR 1 Unauthorized + 2 A/B/C
Activate Hangar, tutor C if not in hand, otherwise tutor B
Summon C, equip with Driver
Remove Driver to equip Torque Tune Gear to C
Unequip TTG, link C + TTG into Halq
CL1 Halq CL2 C, resolve C to summon B or A, tutor Deskbot with Halq
Link Halq + Deskbot into Auroradon, recur Deskbot
Synchro Borreload Savage Dragon with Deskbot + token + A/B (use A to grab back TTG or B to tutor another union)
Activate Auroradon saccing 2 tokens to SS Coltwing, Coltwing returns Deskbot
Synchro Shooting Riser Dragon with Deskbot + 2 tokens
Send missing A/B/C piece off of Shooting Riser Dragon to make it level 3
Synchro Shooting Riser + Coltwing for FA Dawn Dragster
Make ABC
End board - Auroradon, ABC, Borreload, FA Dawn Dragster
Nibiru-proof combo:
Pieces - 1 Hangar + 1 A/B/C OR 1 Unauthorized + 2 A/B/C
Activate Hangar, tutor A if not in hand, otherwise tutor C
Summon C, equip with Driver
Remove Driver to equip B to C
Unequip B, link B + C into Barricadeborg Blocker
CL1 C, CL2 B, CL3 Borg
Pitch A to Borg, tutor TTG with B, SS TTG with C
Link Borg + TTG into Halq, tutor Deskbot with Halq
Link Halq + Deskbot into Auroradon, recuring Deskbot
Synchro Herald of the Arc Light with Deskbot + token
Activate Auroradon saccing 2 tokens to tutor Coltwing, recuring Deskbot
Synchro Deskbot + 2 tokens for FA Dawn Dragster
Make ABC
End board - Auroradon, ABC, FA Dawn Dragster, Herald of the Arc Light, Mecha Phantom Beast Coltwing
Simple ABC combo (not Nib or Ash proof):
Pieces - 1 Hangar OR 1 Unauthorized Reactivation + 1 A/B/C
Activate Hangar, tutor B
Summon B, equip with Driver
Remove Driver to equip B with C
Unequip B, link B + C into Platinum Gadget
Tutor A with B
SS A with Platinum Gadget
Make ABC
End board - Platinum Gadget, ABC
2-card Link Climb:
Pieces - 1 Hangar + 1 A/B/C OR 1 Unauthorized Reactivation + 2 A/B/C
Activate Hangar
If A or C is in hand tutor B, otherwise tutor C
Summon C, equip with Driver
Remove Driver, equip C with A
Unequip A, link C + A into Knightmare Phoenix
CL1 C, CL2 A, CL2 Phoenix
Resolve Phoenix (don't pitch B), use A to recycle C, SS C with C
Link C + Phoenix into Knightmare Unicorn
CL1 C, CL2 Unicorn
Resolve Unicorn (don't pitch B), SS B with C
Link B + Unicorn into Accesscode Talker
CL1 B, CL2 Accesscode
Tutor anything with B
Make ABC
End board - ABC, Accesscode Talker
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