LTT ACFT WITH NO FLT PLAN; REPOSITIONING FROM CHICAGO MEIGS FIELD TO MIDWAY WAS ASSIGNED FIRST TO CONTACT MDW TWR AFTER DEPARTING MEIGS; THEN TWR INSTRUCTED THEM TO CONTACT APCH CTLR. APPARENT LACK OF COORD BTWN ATC FACILITIES WHICH ARE ALL VERY CLOSE TO EACH OTHER.

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WE DEPARTED CHICAGO MEIGS FIELD ENRTE TO CHICAGO MIDWAY (A REPOS FLT). WE DEPARTED RWY 36 FOR A R TURN OUT TO COME BACK OVER MEIGS ENRTE TO MIDWAY. WE LEVELED AT 1900 FT AND WERE RELEASED TO CALL MIDWAY ON THE W EDGE OF MEIGS FIELD. WE CALLED MIDWAY TWR GAVE OUR POS AND INTENTIONS. TWR INSTRUCTED US TO CONTINUE AND CALL APCH. WE CALLED APCH AND AT THE SAME TIME STARTED TO TURN OUT S TO STAY AWAY FROM THE ATA. WE ALSO STARTED DSNDING TO 1500 FT. APCH GAVE US A SQUAWK AND ASKED FOR OUR POS. WE COMPLIED AND TOLD HIM 5 E INBOUND. HE CALLED AND SAID HE SHOWED US 2 1/2 - 3 MI E; AND COMMENTED ON OUR SURPRISE TO THE TWR. WE ADVISED HIM THAT WE CALLED TWR AND WERE ADVISED TO CONTACT HIM. HE GAVE US VECTORS AND GOT US TO THE ARPT FOR LNDG WITHOUT INCIDENT. I FEEL THAT WE COULD POSSIBLY HAVE HAD A LOT BETTER TRANSITION WITHOUT ANY PROBS HAD THERE BEEN BETTER COMS BTWN THE CTLRS (MEIGS TWR; MIDWAY; APCH) AND US. THESE FLTS SHOULD BE NO PROB; AND A SIMPLE CALL TWR-TO-TWR; ETC; WOULD REMEDY SUCH OCCURRENCES.