The plate is 17 inches. At the Major League level that is the strike zone. If any part of the ball crosses over the plate it is a “strike.” That is how the electronic zone you see on tv is calibrated, and how it will be called when they eventually go full electronic. If you’re interested, there is a Twitter account that uses the electronic zone as a reference and grades every home plate umpire across every MLB game for how accurate their strike zone is. It is @UmpScorecads. Here’s an example:
That page grades umps on the strict 17” zone. So if any part of the 3” ball crosses the zone it should be a strike. However, when MLB grades their own umps, they allow calls in an acceptable “shadow zone” which lies at 16.5” to 17.5”, so a quarter inch both on the plate and off the plate on both sides. They don’t consider pitches in this area called incorrectly either way, and their grades reflect that.
There are minor and independent leagues currently using an electronic zone to call balls and strikes that use a zone that is 18” wide, so an extra half inch on both sides of the plate.
Most college and minor league umps are trained at the same level, and they would be instructed to call the game based on a zone that resembles the slightly expanded zone of the minor leagues. Obviously there are inconsistencies, and every ump will see the zone differently, especially in college. On any given conference weekend there will be 33 Power 5 series. That’s 3 different home plate umpires per series, so 99 total different umpires. Add in all the mid-major, low-major, and lower divisions of college baseball, and there are thousands of umpires who will all see the zone differently.
So to answer the question, the plate itself is 17”. There is no “black” on the plate. But at different levels the zone is called differently. The lower you go the wider the zone will get, and the more inconsistent it will get.