However, the curious and controversial fact is to resonate the end fed half wave monopole there needs to be very little current at the feed point. The end of the antenna is a high impedance point. It must be voltage fed as opposed to current fed for a quarter wave monopole.. The return current (enough) can be satisfied with a short counterpoise per AA5TB and Moxon. Note, I am assuming a tuner similar to the one described by AA5TB. There are two sides of the output circuit one for the antenna and one for the counterpoise. The counterpoise could optionally be connected to the coax shield. This would mean that the short run of coax to the rig is the counterpoise in the QRP portable case. I have measured the outside shield current and it is indeed low for a short length of coax to the rig. I have also tried adding a longer counterpoise and it did not affect tuning or the current in the half wave antenna.
W8JI discusses at length feed line currents and the possible downside for a home installation of an end fed Note, that a long feed line is not part of the AA5TB discussion as it is oriented to QRP portable. It seems to me that the low current at the feed point could become part of a standing wave going back to the rig on the outside of the shield. The current would be high at various points and would become a radiator causing pattern distortion. Likewise, you could encounter a high voltage point and get coupling to yourself or other devices in the shack. If I was installing a home QRO antenna I would lean toward a balanced antenna if possible.
I call this territory the tar pit. Just Google end fed half wave for discussion in the forums. Even the masters disagree. So we all have tar on our feet. The bottom line is that an end fed half wave monopole is a popular choice for QRP folks. It is easy to deploy and when you are making contacts at 5 watts it is a good enough antenna in my book. So I have stated my understanding at this point but I am open to further enlightenment in the future.
Note a nice end fed half wave monopole tuner is available from Hendricks QRP Kits.