D10 CTLR EXPERIENCED OPERROR AT 3500 WHEN ADJACENT CTLR; WITH APPROVAL; DESCENDED DFW ARR INTO DEP TFC HANDLED BY REPORTER.

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I WAS WORKING 3 RADAR POS COMBINED: MEACHAM N HIGH; MEACHAM N AND ARR 5 IN A S FLOW AT DFW. WHEN THE ARR 5 POS (WHICH WORKS ARRS TO DFW RWY 13R) WAS OPENED/SPLIT DUE TO TFC VOLUME; I GAVE THE CTLR CTL TO DSND IN MY AIRSPACE REF MY TFC. THIS IS STANDARD COORD THAT ALLOWS THE ARR 5 CTLR TO EXPEDITE DFW TFC AND PREVENTS UNNECESSARY LEVELING OF TFC FOR AIRSPACE RESTRS. I HAD ACFT X; BEECH KING AIR; ON A VECTOR ENRTE TO THE DENTON (DTO) ARPT AT 3000 FT TO PASS BELOW ARR 5 TFC AT 4000 FT; INBOUND TO DFW RWY 13R. I WAS ALSO ATTEMPTING TO MAKE A MANUAL HDOF TO ZFW ON A DIFFERENT IFR DEP THAT WOULD NOT AUTO HDOF. THERE WAS AT LEAST 5 OTHER ACFT UNDER MY CTL ON VECTORS TO VARIOUS ARPTS; AND I WAS VECTORING THE N DEP E TO STAY IN TRACON'S AIRSPACE WHILE ATTEMPTING TO ACCOMPLISH THE MANUAL HDOF. THE ARR 5 CTLR HAD ONLY A FEW DFW ARRS LEFT ON HIS FREQ AND BEGAN TRYING TO HELP ME RAISE ZFW FRISCO SECTOR. HE WAS IN THE PROCESS OF LOCATING AN INDIRECT ACCESS DIAL CODE WHEN HE FAILED TO SEE MY TFC INBOUND TO DTO THAT WOULD CROSS BELOW HIS FINAL FOR RWY 13R AT DFW. HE DSNDED A B737 TO 3000 FT WHICH PUT HIS TFC IN DIRECT CONFLICT WITH MY KING AIR. MY ATTN WAS N OF THAT AREA WITH THE NBOUND DEP. I SCANNED THE AIRSPACE AND SAW THE CONFLICT. BOTH MYSELF AND THE ARR 5 CTLR ISSUED RESOLUTION INSTRUCTIONS SIMULTANEOUSLY: HE CLBED THE B737 AND I DSNDED THE KING AIR. CAUSAL FACTORS: 1) THE FAILURE OF THE AUTO HDOF AND THE CONSEQUENT MULTIPLE CALLS TO ZFW WITH NO ANSWER. 2) HIGHLY CONGESTED AIRSPACE; CREATING AN URGENCY WITH EVERY DECISION/INSTRUCTION TO PLTS. 3) FATIGUE: A) THE ARR 5 CTLR HAS BEEN ASSIGNED AND WORKING 6 DAY WORK WKS FOR MANY MONTHS. B) THE FAA HAS MANDATED AT D10 AND MANY HIGH VOLUME FACILITIES THAT THE CTLRS WORK MORE TIME ON POS. THE EXACT MANDATE IS: 70% OF THE CTLRS ON POS 100% OF THE TIME. THIS DECREASES MENTAL REST TIME IN BTWN RADAR SESSIONS AND INCREASES MENTAL FATIGUE. THIS ATTEMPT TO PROVE 'INCREASED PRODUCTIVITY' IS DEFINITELY ANTI-PRODUCTIVE AND UNSAFE.