ARTCC CTLR AT ZOB ALLOWED A C525 TO ENTER ANOTHER SECTOR'S AIRSPACE WITHOUT A HDOF OR COORD.

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I WAS WORKING THE BLUFFTON SECTOR AT ZOB. I HAD JUST SPLIT BFT OFF FROM THE LORAIN SECTOR (LOR) TO ALLEVIATE TFC IN LOR (APPROX 30 MINS PRIOR TO INCIDENT). I RECEIVED A HDOF ON A C525 REQUESTING FL370 VIA VWV DIRECT TO APE. I MADE A POINTOUT TO LOR AND EVENTUALLY CLBED ACFT TO FL370 THROUGH SW CORNER OF LOR. I THOUGHT THEN THAT I HAD HANDED THE ACFT OFF TO LCK VIA THE AUTOMATED HDOF SYS. I THEN FOCUSED ON A SIT INVOLVING SEVERAL ACFT ON THE WESTERN SIDE OF MY AIRSPACE TOWARD ZAU'S BOUNDARY. THIS SIT REQUIRED SEVERAL POINTOUTS AND COORD CALLS TO RESOLVE. WHEN I RETURNED MY ATTN TO THE C525; TO CHANGE HIS FREQ TO ZID SECTOR (LCK); I REALIZED THE HDOF HAD NOT GONE TO ZID AND THE ACFT WAS PAST THE BOUNDARY; AT WHICH POINT; I CALLED LCK TO MAKE SURE THEY COULD NOW SEE THE HDOF. JUST PRIOR TO THIS INCIDENT; A SIT HAD OCCURRED BTWN LOR AND LCK; THAT NECESSITATED ZID TO SPIN AN ACFT TO FL330. I FEEL THE RESULTING DISCUSSIONS AND CONFUSION WERE A DISTR; SINCE BFT AND LOR SECTORS ARE LOCATED PHYSICALLY NEXT TO EACH OTHER. I FAILED TO NOTICE THAT THE HDOF DIDN'T GO TO LCK IN TIME; AS THE ACFT SPD INCREASED APPROX 70 KTS ONCE HE REACHED FL370. THERE WAS NO MANUAL (RADAR ASSOCIATE) CTLR AND TFC INCREASED FASTER THAN I ANTICIPATED.