What are existing theories on competing wills in the mind? To clarify a little further, I've read in different places that our brain could be composed of mini minds, that preform all sorts of actions.  Assuming this is valid I'd think that of these minds, some result in a composite or layering that results in our personality and an ultimate will that wins out to complete some action or decision, insomuch as a set of minds are inter-related in relation to some function.   

I'm really just assuming from reading various articles and papers and some personal self reflection... but I'd imagine there is something to read in relation to this idea in some shape or form.... In other words I'm looking for more solid reading material, I'm not sure what I should be searching for.
Instead of pointing you to existing theories, which is (1) too advanced for you to understand at the current level of knowledge, and (2) too focused so that you don't have a big picture, why don't we just suggest you to read a textbook about cognition? It will solve both problems at the same time. 

I recommend the book Cognitive Psychology, written by Strenberg, as the starting point. Cognition: Exploring the Science (author: Reisberg) is also a good one. If you are like me, you will realize how to make the question clearer just after some first few pages of reading.