APCH CTLR FAILED TO HDOF SMT TO ARTCC; UNAUTHORIZED PENETRATION OF AIRSPACE.

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I AM AN FPL CTLR AT MGM RAPCON/TWR. I WAS IN THE PROCESS OF TRAINING ON OUR N RADAR SECTOR. THE SECTORS WERE COMBINED BECAUSE IT WAS STILL EARLY MORNING AND THE SECTORS STAY COMBINED UNTIL MID MORNING. THE SUPVR WAS BUSY WITH ADMINISTRATIVE DUTIES (TRAINING OUR NEW FACILITY MGR) AND HAD LEFT AN FPL AS CTLR-IN-CHARGE. THE FPL IN CHARGE HAS 15 YRS EXPERIENCE. I HAVE 4 YRS ONLY 2 YRS RADAR EXPERIENCE. I HAVE BEEN ISSUED THE DUTY OF PRIMARY TRAINING. I WAS TRAINING A YOUNG MAN THAT HAS NO PREVIOUS RADAR EXPERIENCE. HE HAS AROUND 80 TRAINING HRS ON OUR RADAR SECTORS. THE SESSION WAS GOING NORMALLY AND AS SCHEDULED. I ANTICIPATED NO PROBLEMS EXCEPT THAT THE CTLR-IN-CHARGE WAS HAVING TO WORK RADAR DATA AND COULDN'T KEEP UP WITH THE DUTIES OF DATA AND CTLR-IN-CHARGE (CIC). THERE WERE A COUPLE OF OCCASIONS WHEN WE DIDN'T HAVE FLT PLAN INFO BECAUSE OF THIS. I; AS TRAINER; WANTED THE TRAINEE TO WORK MODERATE TFC BECAUSE HE HAS REACHED THE STAGE TO WHERE LIGHT TFC PRESENTS NO CHALLENGE. AND AS IT HAPPENED; THE TFC BUILT RAPIDLY AND I ENDED UP ASKING FOR A SPLIT. THE SUPVR OR CIC USUALLY COORDINATES AND WATCHES AS THE SECTORS ARE SPLIT BUT COULDN'T IN THIS CASE. THE OTHER FPL CTLR WAS SETTING UP THE S SCOPE TO SPLIT THE SECTORS N AND S. HE WAS WATCHING AS WE TRIED TO SPLIT. AT THIS TIME THE TRAINEE WAS STILL SITTING AT N RADAR; BUT I WAS WORKING THE POS. THE FIRST XMISSION I MADE WAS TO AN ACR TO TURN R HDG 360 DEGS CLB AND MAINTAIN 10000 FT. AN MTR ON A MISSED APCH AT MXF ARPT; TOOK THIS CLRNC; ALSO; AND BEGAN A CLB (RAPID RATE) TO 10000 FT. DANNELLY AND MAXWELL ARPTS ARE LAID OUT SUCH THAT CONFLICTS BECOME POSSIBLE ALL THE TIME. ANYWAY; I CAUGHT THAT MTR WAS CLBING AND IMMEDIATELY ASKED WHO ISSUED THE CLB. I TURNED THE MTR IMMEDIATELY TO AVOID CONFLICT WITH THE ACR AND THEY MISSED BY 5 MI. AS I WAS DOING ALL OF THIS; NO ONE WAS WATCHING THE BOUNDARIES AND AN SMT ENTERED ZTL'S (MGM SECTOR ATLANTA CENTER) AIRSPACE WITHOUT A HDOF. AFTER THE CONFLICT OF ACR AND MTR WAS RESOLVED I IMMEDIATELY WENT BACK TO SPLITTING THE SECTOR AND NOTICED THAT SMT HAD NOT BEEN HANDED OFF. I JUMPED ON THE LINE TO ZTL AND TRIED TO COORDINATE. I ALSO FLASHED THE AIRPLANE TO ZTL FOR AN AUTOMATED HDOF. ZTL TOOK THE AUTOMATED HDOF BUT WOULD NOT ANSWER THE SHOUT LINE FOR COORD. THE ACFT WAS NOT IN CONFLICT WITH ANY OTHER ACFT AND NO OTHER PROBLEM OCCURRED. THE ACFT WAS SWITCHED TO ZTL AND I INFORMED THE CIC WHAT HAPPENED. HE TURNED HIS HEAD TO THE INCIDENT FROM RADAR DATA. I REALIZE THAT IT WAS MY FAULT FOR NOT PULLING THE TRAINEE OUT SOONER AND NOT ASKING FOR A SPLIT SOONER BUT; ALSO; FEEL THAT SOME OF THE BLAME BELONGS TO THE SUPVR WHO WASN'T AROUND AND THE CIC WHO HAS MUCH MORE EXPERIENCE AND HAS HELD A TEMPORARY SUPVR JOB AND WASN'T COORDINATING FOR ME AND WATCHING THE TFC.