PA46 VFR DEP FROM TEB IS REFUSED RADAR FLT FOLLOWING FROM N90 AFTER LEAVING TEB CLASS D.

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OCCURRENCE ON A VFR FLT FROM TEB TO FDK. A REQUEST WAS MADE WITH TETERBORO CLRNC DELIVERY FOR A CLASS B CLRNC AND VFR FLT FOLLOWING. CLRNC DELIVERY RESPONDED WITH A DISCRETE XPONDER CODE. TETERBORO TWR (LCL CTL) ISSUED TKOF CLRNC ON RWY 24 AT APPROX XA00 LCL. ACFT DEPARTED MAINTAINING RWY HDG. TWR (LCL CTL) STATED THAT ACFT WAS IN RADAR CONTACT AND INSTRUCTED THE ACFT TO FLY A HDG OF 270 DEGS. THE ACFT COMPLIED. TWR THEN INSTRUCTED THE ACFT TO FLY A HDG OF 300 DEGS. THE ACFT COMPLIED. A REQUEST WAS MADE TO THE TWR FOR A HDOF TO APCH/DEP CTL. THE TWR CTLR RESPONDED 'I'M WORKING ON IT.' AT APPROX XA05 THE TWR CTLR INDICATED THAT A HDOF WAS IMPOSSIBLE 'UNABLE HDOF' AND THAT THE ACFT SHOULD SQUAWK 1200 AND CHANGE FREQS. NO FREQ WAS ASSIGNED. NO HDOF WAS MADE. THE TWR CTLR THEN ANNOUNCED THAT 'ALL TETERBORO DEPS WERE ON HOLD DUE TO SYS SATURATION.' THE PLT THEN TURNED THE ACFT ABRUPTLY TO A HDG OF 240 DEGS; SO AS TO AVOID ESSEX COUNTY (CDW) AND MMU CLASS D AIRSPACE. A HDOF TO DEP; A CLASS B CLRNC; AND RADAR FLT FOLLOWING WAS NEVER PROVIDED. TKOF CLRNC SHOULD NEVER HAVE BEEN ISSUED IF THE SYS WAS SATURATED. IT IS MOST UNUSUAL FOR A TWR (LCL) CTLR TO ISSUE RADAR VECTORS TO AN ACFT.