PLT OF A C421 INADVERTENTLY PENETRATED THE ADJACENT CLASS D AIRSPACE AFTER DEPARTING A NEARBY ARPT.

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I DEPARTED FXE ARPT AT APPROX XA30 ON NOV/XA/00. I TOOK OFF ON RWY 31; MADE A R TURN OUT TO HDG OF 090 DEGS TOWARD FREEPORT; BAHAMAS. I WAS IN A CRUISE CLB AT 1200 FT; APPROX 3-4 MI FROM FXE; ADJUSTING MY #2 RADIO FOR MIA FSS TO PICK UP MY (122.4) VFR INTERNATION FLT PLAN. AT THAT TIME FXE TWR SAID TO CONTACT PMP TWR. I WAS OPENING MY FLT PLAN WHEN I LOOKED DOWN AND SAW A SMALL PLANE TO THE L AND BELOW ME. IT WASN'T VERY CLOSE; BUT I THOUGHT 'I'M IN 2 CLASS D AIRSPACES AT THE SAME TIME -- FXE AND PMP -- I HOPE THE OTHER PLT SAW ME TOO.' AS I CONTINUED TALKING WITH MIA FSS; I WAS HELPING RELAY MESSAGES BTWN AN AN-2 TRYING TO CONTACT MIA FSS FOR A DISCRETE CODE TO ENTER UNITED STATES AIRSPACE. HE WAS LOW AND COULD HEAR ME TALKING TO MIA FSS BUT THEY COULD NOT HEAR HIM SO HE ASKED ME TO RELAY TO MIA FSS. ANYWAY; I HELPED THIS GUY AND MIA FSS. THIS TOOK APPROX 5 MINS AND I WAS WELL OVER THE OCEAN AT THIS TIME. I SHOULD HAVE CONTACTED PMP TWR WHEN THE FXE TWR TOLD ME TO; BUT I WAS TOO BUSY AT THE TIME WITH FLYING THE PLANE AND OPENING UP A VFR FLT PLAN. THE PROB IS THAT THEORETICALLY; 2 CTL TWRS CTL THE SAME AIRSPACE BECAUSE THE 2 ARPTS ARE LOCATED WITHIN 5 MI OF EACH OTHER. I AM VERY INTERESTED IN AVIATION SAFETY. I HOPE FXE AND PMP TWRS TALK TO EACH OTHER ABOUT ACFT IN THE AIRSPACE THAT THEY BOTH CTL.