Power, as referred to in a TPE relationship, is something that resides within the individual. Dictionary.com talks about power as an "ability to do or act". It is the "capability of doing or accomplishing something". A person can not give this away. They can, however, give away the authority to use and guide it. It is like a car that has 500 horse power. When you buy the car or drive the car, you can not take it's power. You can use it though. If you are behind the wheel and the car is running, you have the authority to use it however you see fit. There are ramifications but the car will not say no because it doesn't like what you are doing. Having a slave submit to your will gives the Dominant the authority to command the slave to do anything, within the slaves capabilities, that the slave has given consent to. Total authority exchange allows the Master to command ANYTHING within the slaves abilities and expect the slave to carry it out. It is still the slave, though, that has to carry it out. The power to fulfil the command still resides with the slave.
How then can you have complete control over a slave? The slave must give complete authority to the Master for their capabilities. The more control the slave has over their capabilities, actions, thoughts, behaviours, and beliefs, the more authority the slave is able to give to the Master.
When TPE is looked at in this light, it becomes clear that the only way to truly accomplish it is to train the slave to have complete control over all aspect of themselves. Instead of training a slave to look to the master for control, they must look within. The Master is the guidance not the power. Training a slave to fully utilize their power gives a Master the authority to totally direct and control every aspect of a slave. Instead of seeking for Total Power Exchange, try to achieve Total Authority Exchange.