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If you will be taking it out of state, it will have to be titled and registered. The following is required to do so:
Trailer Title and Registration:
Title or Manufacturer’s Certificate of Origin
Sales Tax (5% of sale price, not to exceed $300)
Form 400 (Forms and Manuals section of scdmvonline.com)
Proof of Insurance (for the vehicle that will be pulling the trailer)
$15 Title Fee
$75 Permanent Tag Fee
Final answer: Since the trailer was salvaged, I can't register it.