BE40 CREW ENTERED LGA CLASS B AIRSPACE WHILE ON A CIRCLING APCH TO TEB RWY 19.

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WE WERE ESTABLISHED ON THE VOR DME-A APCH INTO TEB. PRIOR TO CLIFO INTXN; TWR CTLR INSTRUCTED; 'AFTER CLIFO INTXN; MAINTAIN 1500 FT UNTIL FURTHER INSTRUCTED. ALSO; 170 KTS OR GREATER.' WE COMPLIED. AFTER CLIFO INTXN; BEFORE WE CROSSED OVER THE ARPT; THE TWR CLRED US FOR THE VISUAL; CALLED OUT 2 ACFT AHEAD IN THE LNDG PATTERN AND THEIR POS AT THE TIME; THEN STATED WE WERE '#3; CLRED TO LAND RWY 19.' WE ACKNOWLEDGED. WE CROSSED THE ARPT TO THE ENE; AND BEGAN TO PARALLEL RWY 6/24. WE WERE STILL LOOKING AT 1500 FT AND 170 KTS OR GREATER. THE PF WAS MAINTAINING A R ANGLE TO RWY 19L DOWNWIND BECAUSE WE WERE STILL LOOKING FOR TFC AHEAD AND DID NOT WANT TO TURN INSIDE THAT TFC IN THE PATTERN. (IT WAS DIFFICULT TO SEE BECAUSE OF CLOSENESS TO ALL THE GND CLUTTER OF LIGHTS.) TWR SAID TO SLOW. I (PNF) QUERIED WHAT SPD HE WOULD LIKE. HE RESPONDED 180 KTS. I ADVISED WE WERE AT 175 KTS (HE HAD INSTRUCTED US TO MAINTAIN 170 KTS OR GREATER). SO; I REPLIED; '180 KTS.' (WE THEN HAD TO INCREASE AIRSPD TO COMPLY WITH HIS SLOW-DOWN INSTRUCTION.) I HAD BEEN USING FMS TO MAINTAIN SITUATIONAL AWARENESS WITH PROX TO DOWNWIND. I COULD NOT SEE RWYS FROM MY SIDE OF THE ACFT. I WAS ALSO LOOKING OUTSIDE FOR TFC. MY WORKLOAD WAS DOUBLED BECAUSE ALL OUR LIGHTS BEHIND THE FMS AND FLT DIRECTOR HAD GONE OUT. EACH TIME WE WERE ISSUED A CONFIGN CHANGE; I HAD TO USE A FLASHLIGHT TO DO SO. AT THIS POINT; TWR CTLR YELLED WE WERE TOO FAR N. WE WERE VIOLATING LGA AIRSPACE; TO TURN DOWNWIND. ABOUT 60-90 SECONDS BEFORE HE SAID THAT; WE HAD ALREADY ANGLED BACK TO THE L AND ONTO A L DOWNWIND FOR RWY 19; BUT ONLY AFTER OUR TFC WAS IN SIGHT TO OUR L. I DOUBLE CHKED THE FMS AGAIN. AT NO TIME WERE WE EVER MORE THAN 3 MI FROM THE CTR OF TEB; HDG APPROX 070 DEGS. OUR IMPRESSION WAS THE TWR WAS CONFUSED ABOUT THE INSTRUCTIONS HE WAS ISSUING TO US. IMMEDIATELY PRIOR TO THE L BASE TURN; TWR AGAIN SAID; 'I NEED YOU TO SLOW!' I RESPONDED WE WERE AT 140 KTS. ONCE AGAIN; HE CLRED US TO LAND. THEN HE CAME BACK AS WE WERE IN OUR TURN AND SAID; 'I TOLD YOU TO MAINTAIN 1500 FT. CONFIRM YOU ARE NOW AT 1000 FT.' I RESPONDED ONLY; 'UNDERSTAND WE ARE CLRED TO LAND RWY 19.' WHEN I HAD OBSERVED PF BEGINNING DSCNT; I STARTED TO ADVISE HIM TO STOP (I SAW HIM TURN THE ALTITUDE PRE-SELECTOR AND SIMULTANEOUSLY BEGIN DSNDING). HOWEVER; I THEN REALIZED WE HAD ALREADY BEEN CLRED FOR THE VISUAL ONCE AND TO LAND TWICE; THEREFORE; HE WAS ACTING APPROPRIATELY. AS WE CROSSED THE RWY THRESHOLD; 50-75 FT; THE TWR INSTRUCTED A 'GAR!' THE PRECEDING ACFT HAD NOT CLRED THE END OF THE RWY. WE COMPLIED. ON UPWIND; TWR INSTRUCTED; 'MAKE L TFC; RWY 19; CLRED TO LAND.' WE ACKNOWLEDGED AND COMPLIED. AFTER TOUCHDOWN; TWR INSTRUCTED US TO CLR (EXIT) TO THE R AND CONTACT GND. I DOUBLE CHKED THE CLASS B AIRSPACE FOR LGA. AT 1500 FT; HDG 070 DEGS; PARALLELING RWY 6/24 AT 3 NM; WE WERE NOT IN CLASS B AIRSPACE. ALSO; AFTER 2 LNDG CLRNCS; I DO NOT BELIEVE WE VIOLATED ANY ALT RESTR.