Breathing per se is a dull subject, and even mastery of it will not insure good singing. Athletes frequently have enlarged their vital capacity to maximum, can hold their breath longer than most singers, and are are otherwise superior in this department, but still sing poorly. Also fine singers can be found whose technique is unorthodox, even poor. The important part is coordinating the breath pressure with the vibrator, which Louis Bachner called “hookup”. This is epitomized in the attack. A lesson on breathing should never consist of silent breathing exercises only. They should always be followed by practice in correct attack.
Vennard, William. Singing: the mechanism and the technique. Carl Fischer, LLC, 1967.