A ZKC controller described a confused hand off event when RZC TRACON accepted a hand off initiated and planned for ZME. The reporter noted directed automated hand off procedures need to be changed in the facility software.

Narrative

Aircraft X was cleared from EOS direct FSM. On departure my trainee gave the plane a heading of 270 for traffic; climbing to FL190. At about FL180 the aircraft was cleared direct FSM. A hand off was initiated by pressing 'M' (for Memphis). I was unaware that the data block was flashing at RZC Approach. Although RZC Approach only has airspace at or below one five thousand; they took the hand off. The plane's communications was changed over to ZME. I noticed the hand off was not made to ZME right before the plane reached the boundary. I called ZME. I asked if they had a hand off on Aircraft X. They said it was taken care of. The sector was manned by a trainee; myself (instructor) and a newly checked out D-side only. There has been an on going problem with hand offs going to RZC Approach instead of ZME; with aircraft climbing above approach airspace. It is something one has to be aware of. Although I gave it some thought when we departed the plane from EOS; it got by me when it counted. I would like to see aircraft that file an altitude above RZC Approach have an automated hand off go to ZME instead of approach. I also have to question why RZC Approach would accept a hand off on an aircraft that is not in their altitudes. They had no reason to believe that aircraft was going to enter their airspace.