The minimum and maximum width of the slot are not usually specified by code but by the manufacturer's installation instructions. The code will let you figure out the minimum square inches of net free vent area NFVA) that you need.

The manufacturer makes a vent that has a certain amount (in square inches) of net free vent area per lineal foot of ridge. This sets a limit on how narrow the slot can be, so that the vent and not the slot is the limiting factor on air flow through the vent. The vent itself will be made to a certain width and only extends to cover the roof a few inches on either side of the ridge. The manufacturer will specify a maximum slot width which, if not exceeded, should ensure a watertight joint between the vent and the roof covering.

Let's go back to that minimum slot width again and see how narrow it could be. I've seen typical ridge vents with NFVA as low as 9 sq in per ft of ridge and as high as about 18-20. Take that low flow vent at 9 sq in/ft. If you use that one, you need at least 9/12 or 3/4" total width of a slot (clear of the ridge board) or 3/8" on either side of the ridge. This is to ensure that the vent, and not the slot, is limiting air flow. Take a higher flow vent at 18 sq ft/in. On that one you need 18/12 or 1.5 inches minimum total width (clear of the ridge board) or 3/4" on each side if the ridge. Cutting slots wider than the minimum based on the NFVA of the vent you are using does nothing to increase ventilation; it increases the chances that the vent will leak.

Check on Jerry's math:

2006 IRC 806.2 has the requirements.

Let's assume a gable roof and our ventilated space (inside the attic) is 40 feet long (at the ridge) by 30 feet wide (eave to eave) or 1200 sq ft.

Using 1/150, the required total NFVA is at least 8 sq ft. Using 1/300, it is at least 4 sq ft.

Let's assume worst case of NO soffit vents and either no vapor barrier or one with an effective perm greater than 1. If we cut a slot along the entire length of the ridge inside the gable end walls (assumed to be 40 feet), we would need a minimum clear slot width (8 sq ft / 40 ft) x (12 in/ft) = 2.4 inches (total on both sides of the ridge board). For this to work, we'd need to find a vent that provided at least 29 sq inch NFVA per foot of ridge. (Note - some manuf say you couldn't do this configuration with their vents, because their install instructions specify use of their vent in conjunction with soffit vents.)

Let's assume a more typical case where we have soffit vents and they provide at least 50 percent of the required NFVA. Now we can use 1/300 which requires 4 sq ft total. We are going to meet that by providing 1 sq ft at each soffit and 2 sq ft at the ridge. Our slot running the full length of the ridge (inside the gable end walls) can be reduced to (2 sq ft / 40 ft) x (12 in/ft) = 0.6 inches (total on both sides of the ridge board). For this to work, we'd need to find a vent that provided at least 7.2 sq inch NFVA per foot of ridge and run it the full 40 feet.

Let's say we want to use one of those low profile ridge vents with the filter inside, that provides NFVA of 9 sq in/foot. For this vent we would need a slot 3/4 inches wide and (2 sq ft x 144 sq in/sq ft) divided by (9 sq in/foot) = 32 feet long. Use one of those higher flow ridge vents (NFVA of 18 in/foot) and you need a slot 1.5 inches wide (3/4" on each side of ridge board) and only (2 sq ft x 144 sq in/sq ft) divided by (18 sq in/ft) = 16 feet long. In theory, you could use that higher flow vent on a 3/4 inch slot if you ran it for 32 feet. BUT code says you must follow the manufacturers instructions and they will tell you how wide of a slot to cut for their vent.