Here's my recent upgrade experience:
- Flight is LAX-IST, dep on 02-Mar
- I knew online that they had J1, D1, C1 seats available, as well as plenty in Comfort class
- 3 days before the flight I had just turned Elite Plus.
- at the airport checkin, I ask for complimentary upgrade, and I am denied
- I ask for upgrade with miles, I am being sent to Ticketing desk (10m away) for processing
- after 15 minutes of wait and research, lady confirms availability, and tells me that I can choose between using 22.5k miles or 1/2 yearly free upgrade certificate. I opt for the free cert, and within 10 minutes I have my boarding pass with seat 1A on it

Additional learning:
- at the airport, they can process upgrade with miles/certificates, regardless of the fare class available in business; it is based on physical availability, not fare
- the TK systems are still behind, so do expect some time to get your upgrade processed...
- upgrade is per sector, not per journey. My 1-hr connection from IST was in eco... Could be relevant if you have 2 long-haul flights...
- upgrade from Comfort (can be cheap A fare) to Biz (any fare) just became my favourite perk with TK For the really long routes like NRT, LAX, GRU you basically spend the miles you earn, if you upgrade just one leg of the journey.