You can get autopilot disconnects that result in out of trim conditions in either direction, and even an autopilot disconnect where the airplane is perfectly trimmed... depends on how the autopilot disconnect occurred.
Here's how that works: As receivers approach the tanker, the autopilot or the tanker pilot flying autopilot off A/R needs to put in nose up trim. This is because the "bow wave" off of the receiver reduces the downwash on the tail of tanker, reducing the angle of attack of the horizontal stabilizer and hence reducing the tail-down/nose up force from the tail. I haven't seen any math on the subject, but I believe the effect goes something like the square of the distance from receiver to tanker, because the change from 50' ('pre-contact' or 'astern' position) to 40' feels much less than the difference from 10' to 'contact'. And once in contact, when the receiver is high or forward in the envelope, that typically requires an additional click of trim (autopilot off) compared to a receiver in the perfect position (30 degrees elevation and 12' boom extension). With the autopilot on, the autopilot puts in, or takes out that trim as required.
The tanker autopilot applies trim at approximately 1/7th the speed of the pilot's trim switch. So if the receiver closes too fast, the autopilot will be unable to trim nose up fast enough to keep up with the change, and when it gets out of trim it gives up and clicks off. This leaves the tanker pilot with a yoke that's about 30lbs. out of trim in the nose down direction.
If on the other hand, the receiver was in position and quickly moves either AFT or DOWN in the envelope, then they will quickly reduce the bow wave effect and the airplane will be out of trim in the nose up position. If that happens quick enough, the autopilot gives up and leaves the pilot with about a 30lbs. yoke force in the nose up direction. This typically occurs during a break away, especially with a heavy receiver. The autopilot clicks off and the tanker climbs.
The last possibility is that the autopilot has been keeping up just fine, but has some kind of an internal data malfunction or issue and clicks off with the airplane in trim. I've had lots of the other two versions, mostly disconnects in the nose up direction, but I've only had this one once. Our book reads that at any autopilot malfunction when the receiver is closer than 'precontact,' the pilot should 'consider initiating a break-away.' Most guys read this to mean that a break-away is not absolutely required on every autopilot disconnect, so if the autopilot kicks off but everything is perfectly trimmed, guys will instead tell the boom to do a disconnect and back out the receiver, rather than saying the b-word.
The last effect that I haven't yet mentioned is the boom itself. The boom acts like a control surface, except that the boom operator moves is all over the place without telling the tanker pilot. In general, the perfect position is 30 degrees down elevation, and 0 degrees left and right. In that position, I basically set the throttles and have the plane trimmed up and feel really little to nothing from the boom itself (but of course feel the receiver bow wave if he's present). This position requires the boom operator to hold some weight in his hands because the boom does not trim off completely. If the boom operator is lazy and lets the boom hang at near the bottom elevation limit (40 degrees down elevation), then there is more drag on the airplane and it will gradually slow down. If the boom operator raises the boom to near the upper limit (20 degrees) then the airplane will have less drag on it and gradually speed up. Both of these effects require a trim change as well, but the rate of change is typically a little slower than the change required by the receiver. And if the boom should move from the center to the side, then that acts like a rudder left or rudder right input on the tanker, and the autopilot typically responds with a coordinated and opposite rudder and yoke input in the other direction. A tanker pilot flying autopilot off, however, probably just puts in yoke to keep the wings level (i.e. opposite the deflection of the boom).
Autopilot off A/R is kind of like flying along with someone at the other set of controls constantly putting in random trim inputs and stepping on the rudder without telling you. Which can make it difficult to fly a nice stable platform. So if the receiver pilot sucks, the tanker pilot's job gets harder and he will fly worse. And of course, if the tanker pilot sucks, the receiver pilot's job will get harder and he will fly worse. So it can sometimes be tough to assign blame on autopilot off AR, because it's a game of 'screw your buddy.' Autopilot ON, however, blame automatically goes to the receiver pilot or perhaps the boom operator (at least in my eyes, but of course I'm biased), because all the tanker pilot controls is the thrust setting. Provided he's not moving the throttles during the closure from precontact to contact, and provided he only moves them very small amounts very slowly at other times, the receiver should not see any major movements from the tanker.
Oh, one last word about the tanker autopilot for the few guys out there who are receivers: for turns, we have a roll knob that commands a bank angle on the autopilot, but the knob has a detent at 0 degrees of bank. In order to command a turn, you have to get the roll knob out of the detent and then move the knob to the desired bank angle (which we typically try to limit to 15 degrees with heavy receivers). We'll sometimes take fighters to 30 degrees of bank if we have to, but usually we try to keep them at 15 also. Anyways, we try to put in that bank slowly and smoothly by turning the knob slowly... unfortunately, right as the knob leaves the detent, the autopilot puts in the first 3 degrees of bank or so pretty rapidly. So if you are in the back tanking, you will probably see a "head-fake" to the left and then the left turn come in nice and slow. Same thing in reverse as we roll out of the turn: nice and slow to about 3 degrees of bank or so and then a quick whip back to 0, with possibly an overcorrection to 1-2 degrees of the opposite direction bank that quickly disappears. I wish there were some way to prevent that, but unfortunately that's the crappy 1970's technology that we're stuck with.
