UNAUTH TKOF CREATES A POTENTIAL AIRBORNE CONFLICT BTWN A BE1900 OFF RWY 13L AND AN ERJ LNDG ON RWY 17L AT DFW; TX.

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WE EXPERIENCED A RWY INCURSION/TFC CONFLICT DURING THE DEP PHASE OF OUR FLT FROM DFW. DURING OUR TKOF ROLL; WE OBSERVED AN ERJ-145 XING THE DEP PATH OF RWY 13L AS THE ERJ MADE ITS FINAL DSCNT FOR LNDG ON RWY 17L. AFTER BEING CLRED FOR TKOF; THE CAPT TAXIED ONTO RWY 13L AND XFERRED THE FLT CTLS TO ME. I THEN PROCEEDED TO APPLY PWR FOR TKOF AND COMMENCED MY TKOF ROLL. SHORTLY AFTER V1 WAS CALLED; WE OBSERVED THE ERJ XING THE DEP END OF RWY 13L FROM L TO R AT A DISTANCE OF APPROX 3000-4000 FT. UPON OBSERVING THE LNDG TFC; I ROTATED AGGRESSIVELY AND CLBED RAPIDLY TO AVOID ANY POSSIBILITY OF A COLLISION. SHORTLY AFTER OUR INITIAL CLB; DFW TWR INFORMED US THAT WE HAD NOT BEEN CLRED FOR TKOF TO WHICH I REPLIED TO TWR THAT WE HAD RECEIVED A TKOF CLRNC. THE CTLR THEN XFERRED US TO DEP CTL; AND WE CONTINUED THE FLT TO ELD WITHOUT ANY FURTHER INCIDENT. ALTHOUGH THE 2 ACFT WERE NEVER IN POS TO COLLIDE WITH ONE ANOTHER; THE POSSIBILITY OF A COLLISION WOULD HAVE BEEN MUCH GREATER HAD I APPLIED PWR FOR TKOF SOONER OR THE ARRIVING ERJ HAD BEEN CLOSER TO TOUCHDOWN. CONTRIBUTING FACTORS TO THE CONFLICT WERE HIGH WORKLOAD ON BOTH US AND THE CTLR; AND OUR FAILURE TO OBSERVE THE CONFLICTING TFC AS IT MADE ITS APCH TO LNDG. ALSO; NOT HEARING THE CONVERSATION BTWN THE TWR CTLR AND THE LNDG TFC CONTRIBUTED TO THE EVENT THAT TRANSPIRED SHORTLY THEREAFTER. IN MY OPINION; THE CTLR'S INABILITY TO MAINTAIN SITUATIONAL AWARENESS WAS A DIRECT FACTOR TO THE INCIDENT AND THE PRIMARY CAUSE. FROM A CREW STANDPOINT; ACTIONS THAT MAY HAVE PREVENTED THE SIT WOULD HAVE BEEN BETTER VISUAL SCANNING FOR THE LNDG TFC AND A MORE ATTENTIVE EAR TO THE TWR FREQ. ALSO; BY LIMITING THE CTLR'S WORKLOAD TO ALLOW FOR A MORE EFFECTIVE FLOW OF TFC AND PREVENT REPETITIVE ACTIONS THAT CONTRIBUTE TO THE CONFLICTING CLRNCS.