hmm.  still confused and not sure I'm going to be flipping coins back and forth.  If I mined them, and they were free/pennies, might make sense.

If one has an offline wallet with 1 bitcoin that cost me $1000, for example
and then the fork occurs...

How do I then have 1 Bitcoin Core and 1 Bitcoin Unlimited?

If I do nothing, my wallet still remains - when I scan my QR code, what will it tell me?

Will my old Bitcoin coin show up as Bitcoin Core or Unlimited or Classic?

If I import this offline wallet back into an exchange, what does it do?  Where does it go?