If you're checking luggage, show the agent at the check in counter your connecting ticket receipt, so they'll check the bag to your final destination. When you get into HKG, you'll need to go to that airline's check in counter to get your boarding pass, then make sure you show them the baggage claim receipt so that put the number into their system. I connected CO to CX (not same network) and I had no problem. I was in Biz on CX, so I was able to go on the CX site to book a seat. You can also order a special meal online (they have them all, unlike CO).