Submission in Buddhist teachings / practices I have heard people, Buddhists I guess you would say, mention submitting to a higher power. It was just in passing, but I wondered if that sort of thing had any role to play in the theory or practice of Buddhism.

I think I would like to "submit", and can do so without losing my mind etc.. Well, I don't know if that makes any sense, but thanks for any guidance.
The idea of surrender in Buddhism in general can vary very, very widely, depending on the particular ideology. Some ideologies believe you need to submit totally to a Guru to be enlightened, others do not. It depends on how people have set the system up in the first place. Pureland Buddhism is particularly strong about this point, and I encourage you to look it up.

That being said, it is important to mention that Buddhism is not, at its core, about believing in something or submitting to an ideology.. it is about The Dialectic or Conversation that happens when you try something, find out it is not quite as described, then ask a question about your personal experience and get a clarifying answer, or engage in a debate. That is the dynamic. Discovery through experience, discussion and debate.

So, submission and dominance fall then to the status of Dualistic Thinking, and are no different than black and white, cold and hot, or back and front. Both are illusory... Maya (http://en.wikipedia.org/wiki/Maya_(illusion)).

Surrender in the Buddhist sense, on the other hand, is about letting go of any fixed notion of self, the universe or any other idea, and trusting in experience to guide you to truth. It doesn't mean that you give up.. it means you let go of the strong attachment you have to particular ideas about the world and yourself, and allow mind and body to take you to places where you can experience truth.