TPA CTLR VOICES CONCERN REGARDING THE FAILURE OF STARS EQUIP TO AND OFF ACFT TO THE APPROPRIATE ZMA SECTORS.

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I EXPERIENCED A FAILURE IN OUR STARS AUTOMATION DURING THE AUTOMATED HDOF OF EACH OF THESE ACFT. THIS OCCURRED AS 2 SEPARATE INCIDENTS. DURING THESE HDOF AUTOMATION FAILURES MY SECTOR WAS VERY BUSY AND DID NOT HAVE AN ASSISTANT HELPING ME DUE TO OUR STAFFING SHORTAGE. IN THE FIRST INCIDENT A KC35 DEPARTED MCF TO RSW AND POINTS S. ITS REQUESTED ALT WAS 5000 FT. THE REMARKS ON THE FLT PLAN SHOWED A REQUEST FOR PRACTICE APCHS AT RSW. RSW APCH CALLS MY SECTOR TO ADVISE THE KC35 THAT RSW CANNOT ACCEPT HIM FOR PRACTICE APCHS BECAUSE OF A LACK OF STAFFING. I ADVISE THE KC35 AND HE REQUESTS FL290 AND TO CONTINUE ON HIS FILED RTE. WE AMENDED THE FLT PLAN IN THE FIDO. I HANDED OFF THE KC35 TO ZMA AND INSTRUCTED IT TO CONTACT ZMA. APPROX 10 MINS LATER THE KC35 CONTACTS ME AND INFORMS ME THAT ZMA TOLD HIM TO RETURN TO MY FREQ. I CALLED ZMA AND THEY TOLD ME THAT THEY DID NOT KNOW OF THE KC35. THE KC35 WAS LEVEL AT 12000 FT 18 NM INTO ZMA AIRSPACE. THE STARS AUTOMATION HANDED THIS FLT OFF TO SOMEONE AND SOMEONE IN ZMA ACCEPTED THE HDOF. I INFORMED THE FRONT LINE MGR ON DUTY AND HE TOLD ME NOT TO WORRY ABOUT IT. THIS WAS A DANGEROUS SITUATION. NO ONE WAS WATCHING THIS FLT FOR 18-25 NM. THE SECOND INCIDENT OCCURRED LATER IN DAY WITH A CPR G3. THE STARS AUTOMATION WAS HANDING THE ACFT OFF TO THE WRONG SECTOR. ZMA WOULD NOT ACCEPT THE HDOF AND I HAD TO TURN THE ACFT TO AVOID ENTERING ZMA AIRSPACE. HE CALLED THE ON DUTY FRONT LINE MGR AND HE DID A MANUAL HDOF WITH ZMA.