ACFT Y'S UNAUTH RWY ENTRY CREATES NEED FOR LNDG ACFT X TO PERFORM A GAR. ACFT Y STOPS SHORT OF RWY BUT OVER HOLD LINE. TWR CITES RESPONSE TO WRONG CALL SIGN AS INITIAL CAUSE OF INCIDENT.

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ON SHORT FINAL; VISUAL APCH TO RWY 22 LGA AND CLRED TO LAND; MY FO WAS FLYING THE ACFT. I NOTICED AN ACFT Y MD80 TAXIING WBOUND ON TXWY P OR TXWY G (NOT SURE WHICH) AND APCHING THE INTXN OF RWY 22 AT A FAST RATE. THERE WAS DOUBT IN MY MIND THAT HE WAS GOING TO HOLD SHORT OF THE RWY. AS I CALLED OUT THIS FACT TO MY COPLT; LGA TWR REPEATEDLY TOLD ACFT Y TO STOP; STOP; STOP! WE WERE THEN INSTRUCTED TO GAR AND A REJECTED LNDG WAS MADE WITH OUR ACFT TOUCHING DOWN MOMENTARILY IN THE PROCESS. AS WE WENT AROUND; I NOTICED (OUT OF THE CORNER OF MY EYE) THAT ACFT Y HAD IN FACT COME TO A STOP; BUT IT APPEARED TO BE WELL PAST THE HOLD SHORT LINE. I LEARNED TODAY THAT THE REVIEW OF THE TAPES SHOWED THAT THE TWR CTLR CLIPPED A XMISSION INSTRUCTING ACFT Z (AHEAD OF ACFT Y) TO CROSS RWY 22. ACFT Y INCORRECTLY ASSUMED THE XMISSION WAS FOR THEM AND READ BACK THE CLRNC; WHICH WAS NOT CAUGHT BY THE TWR CTLR. THE ACFT Y CREW WAS OPERATING UNDER THE ASSUMPTION THAT THEY WERE CLRED TO CROSS RWY 22. THE FO WAS APPARENTLY NOT LOOKING OUT HIS WINDOW AS THEY APCHED THE ACTIVE RWY OR HE WOULD HAVE SEEN US ENTERING THE LNDG FLARE! SUPPLEMENTAL INFO FROM ACN 340951: BLOCKED OUT OF GATE LGA FOR FLT TO STL. ATIS RPTING DEPS ON RWY 31. TAXI INSTRUCTIONS WERE TO TAXI TO RWY 13; HOLD SHORT OF RWY 22. SUBSEQUENTLY; JUST AFTER THE HAND SALUTE FROM THE PUSHBACK COORDINATOR; TAXI INSTRUCTIONS WERE REVISED TO HOLD POS; ALLOW SAAB ACFT TAXIING S ON TXWY A TO PASS; THEN TAXI TO RWY 13; VIA TXWYS A; J; AND B. FOLLOW THE B737 ON TXWY B; HOLD SHORT OF THE CONCRETE AFTER XING RWY 22. DURING TRANSITION FROM TXWY A TO TXWY B; THE B737 WAS OBSERVED XING RWY 22 ONTO THE CONCRETE PAD. AS THE FO WAS NOW BUSY WITH COMPUTING TKOF DATA FOR RWY 13; I INCREASED MY OUTSIDE VISUAL SCAN AND OBSERVED AN AIRBORNE B727 IN THE LNDG CONFIGN A FEW FT ABOVE THE TOUCHDOWN OF RWY 22. I ABRUPTLY STOPPED SHORT OF RWY 22. THE B727 PASSED BY AIRBORNE. I BELIEVE THE GND CTLR HAD THE PERCEPTION THAT THE TAXI INSTRUCTIONS GIVEN INCLUDED THE ADDENDUM; 'HOLD SHORT OF RWY 22' ISSUED IN THE PREVIOUS CLRNC. SUPPLEMENTAL INFO FROM ACN 340841: OUR INITIAL TAXI CLRNC WAS TO HOLD SHORT OF RWY 22 ENRTE TO THE TKOF RWY 13. HOWEVER; SOON AFTER TAXI BEGAN; WE WERE CLRED BY GND CTL TO CROSS RWY 22. I ACKNOWLEDGED THE CLRNC. BECAUSE OF SEVERAL MINOR COCKPIT DISTRS; I DID NOT PERFORM MY NORMAL OUTSIDE CLRING AS WE APCHED THE LNDG RWY. THOSE DISTRS INCLUDED: A TKOF RWY CHANGE FROM THAT BROADCAST ON ATIS DISCOVERED AS THE TAXI BEGAN AND REQUIRING A TKOF CHART REVISION AS WE TAXIED; ACCOMPLISHMENT OF TAXI CHKLIST -- WHICH I READ; AND AN ACM HAVING DIFFICULTY CLOSING/LOCKING THE COCKPIT DOOR. THESE ALL OCCURRED ON A SHORT TAXI KEEPING ME VERY BUSY. IT WAS A SOBERING REMINDER FOR ME THAT EVEN THOUGH WE WERE CLRED TO CROSS THAT RWY; I CANNOT ALLOW ANY DISTRS TO KEEP ME FROM OUTSIDE CLRING. THE INCIDENT WOULD NOT HAVE PROGRESSED AS FAR AS IT DID HAD I BEEN DOING MY NORMAL LOOKING AROUND. ALSO CONTRIBUTING: THIS WAS MY FIRST LEG BACK AFTER ABOUT 3 1/2 WKS OFF FOR VACATION. EVEN THOUGH I FELT MENTALLY PREPARED; RESTED; AND HAD SPENT TIME REVIEWING THE FLT HANDBOOK; MY PACING/TIMING WAS AFFECTED BY THE TIME OFF. EXTRA DILIGENCE REQUIRED!