First, as per BCAPL rule 1-35 Position of Ball - The position of a ball is determined by its base (see Diagram 7).
Second, as per BCAPL the definition of Head String: a line along the bed of the table, aligned between the second diamonds of the long rails as counted from the head of the table. The area behind the head string does not include the head string.
Third, when placing ball in hand behind the head string BCAPL rule 1-36 Shooting with Ball in Hand Behind the Head String - 3. When you have ball in hand behind the head string, it is a foul if you place the ball outside of the kitchen and shoot.
So, the head string is not part of the kitchen. When you place the cue ball for the break (or for ball in kitchen after the break), you CANNOT put the cue ball dead nuts on the line - it must be behind the line.
Furthermore, if you have ball in kitchen (i.e. after the break) you CAN shoot a ball that is dead nuts on the line because it is out of the kitchen because the line is not part of the kitchen.
A few years ago, BCAPL rules used to state that, when placing ball in hand behind the head string, if you placed the cue ball relatively close to, but past the line (i.e. with a ball width), your opponent had to warn you or it wouldn't be a foul. The old rules went on to say that if a player had ball in hand behind the head string, but placed it "clearly and obviously" outside the kitchen, no warning was necessary and it would be a foul. They must have changed the wording as I can't find those specific words right now.
Finally, if you were over the line, it is a foul. However, they have to prove you were over the line. If no proof exists, or there wasn't a referee present, favor goes to the shooter.
