Big doubt of the day. For maximum power transfer we use a source impedance equal to the load impedance (conjugate for AC, to be exact). We match for reflection too, but that's another story.
Assuming resistive matching half of the power is on the load side, half on the source side and, with a transmission line, assuming it's lossless and matched, nothing on the trasmission line.
However, usually, matching on the source and/or the load to the line is done reactively (transformers, LC, tees, and so on), with narrow band matching being the theoretical optimum (as in, perfect match assuming perfect components).
How is the power balance in that case? Do I simply use phasors so that the inductive and capacitive reactive power just cancel each other (didn't do the math but that should justify it)? In this case (perfect components and lossless line) the only real power loss would be on the real impedance of the source and the rest should be `usefully' available on the real impedance of the load.
Am I missing something?