The only way to hand off control of your breathing to your subconscious is to do something that distracts your conscious mind. You can't focus on breathing and then say, "here you go, brain, handle it."
I don't think that's true. When I started breathing meditation, it felt like that for me: whenever I was aware of my breathing, I automatically switched to directly controlling the breath. As a result, my rhythm was off and I often became lightheaded and stopped.
At some point you learn to separate action and observation: you can focus your attention on the breath, meaning the sensations associated with breathing (air flowing through your nostrils and over your upper lip, belly slowly moving), and still let your body control the breathing action automatically.
In The Mind Illuminated, there is a comparison of this to catching a ball: instead of seeing the ball and trying to directly control your arm to catch it, you focus on your intention ("Catch the ball") and let your body simply act on (implement) this intention.
The great thing is that while you practice this separation of action and observation using the breath, it will apply generally to your life. Very powerful for managing your emotions: instead of being your emotion when you become aware of it, and identifying with the urge to act on it, you learn to observe the emotion without that observation having direct effects on your actions. You can choose to act on it, or choose not to.
