If you buy a property in an arms-length transaction, the assessor will have a hard time justifying a fair-market value that is higher than the purchase price. If that happens, I would appeal. You would most likely win on appeal.
If you do a related-party deal or get a sweetheart deal then the asssessor will most likely use FMV.
The assessor is known to make mistakes so challenging their valuation is not a big deal.
