Starting in 1939, plates got smaller, and started using different numbering configurations.
The letters on the left side are still a county code.

COUNTY CODES 1939

AA-AT = Atlantic	HA-IZ = Hudson	MA-MZ = Monmouth	SK-SU = Somerset	WT-WZ = Hunterdon
AU-AZ = Burlington	JA-JZ = Essex	NA-NZ = Union	SV-SZ = Sussex	(YA-YZ = Essex)*
BA-BZ = Bergen	KA-KZ = Middlesex	PA-PZ = Passaic	UA-UZ = Union	ZA-ZJ = Gloucester
CA-CZ = Camden	LA-LU = Mercer	RA-RZ = Bergen	VA-VZ = Morris	ZK-ZU = Cumberland
EA-FZ = Essex	LV-LZ = Ocean	SA-SJ = Salem	WA-WS = Warren	ZV-ZZ = Cape May

In "THE BULLETIN ALMANAC AND YEAR BOOK FOR 1941", the prefixes are listed as:
Atlantic County - AA-AN
Burlington County - AO-AZ
* The YA-YZ prefix for Essex County was not listed in this almanac, so apparently the YA-YZ prefix was instituted after 1941.

From "List of License Plates Assigned to Agencies - 1952" (Division of Motor Vehicles)
These prefixes were for the A/A 000 and A/A 00A series initially issued in 1952.

COUNTY CODES 1952

AA-AL = Atlantic	HA-IZ = Hudson	MA-MZ = Monmouth	SI-SU = Somerset	WT-WZ = Hunterdon
AM-AZ = Burlington	JA-JZ = Essex	NA-NZ = Union	SV-SZ = Sussex	YA-YN = Passaic
BA-BZ = Bergen	KA-KZ = Middlesex	PA-PZ = Passaic	UA-UZ = Union	ZA-ZK = Gloucester
CA-CZ = Camden	LA-LS = Mercer	RA-RZ = Bergen	VA-VT = Morris	ZL-ZV = Cumberland
EA-FZ = Essex	LT-LZ = Ocean	SA-SH = Salem	WA-WH = Warren	ZW-ZZ = Cape May

Long plates had the county code and 4 digits.
These ranges were issued in 1952:

BA1000-BE9999 = Bergen	LT1000-LT3999 = Ocean
CA1000-CC6999 = Camden	MA1000-MB9999 = Monmouth
EA1000-EH5999 = Essex	UA1000-UB4999 = Union
HA1000-HC9999 = Hudson	ZL1000-ZL5499 = Cumberland
KA1000-KA2999 = Middlesex	ZW1000-ZW3499 = Cape May
LA1000-LB8999 = Mercer

Additional prefixes and numbering patterns were issued between 1953 and 1956.