KA was established by CX as a subsidiary. It is closely held between CX, Swire and CITIC.
It was originally established in order to divvy up China and Taiwan flying. CX was not going to be permitted to continue flying to both the mainland and Taiwan. Rather than give up one, they turned over all their mainland flying to a subsidiary, and kept the Taiwan flying (since it fit better with their established North Asian structure).
Over the year's KA has picked up some additional flying--mainly smaller Asian centres like Hiroshima. After the handover in 97, CX turned over KHH so that there was again a Hong Kong carrier serving both Taiwan and the mainland.