Surely that's the answer by definition: if, when you take over, v<v1 - abort. if v>v1 - keep going.
Many firms, my own included, subdivide the region below V1 into considerations based on what's going on. A general rule, used by us and many others, is any malfunction or problem up to 80 knots will be considered for a rejected takeoff, but above that speed, only for engine fire, engine failure, loss of directional control, or an outward opening door. So it's not quite so simple as rejecting for anything less than V1.
Incapacitation can take many forms. I've had a lack of response due to an ICS failure, lack of response due to me choking on an errant popcorn kernel. That's why there's a second challenge. On two occasions in my career I've had reason to take control from the other pilot, only one on a takeoff, and in that case I didn't actually take control. It was in a small transport category airplane, a Learjet, and involved a non-responsive pilot during a takeoff.
In that case, I was first officer, and in the right seat (I say that because in corporate and charter operations, the F/O may be in either seat, depending on the company policy and practice). The captain was new, inexperienced, and a direct hire captain. He had a track record of poor decisions and problems with other crews, each of whom had reported him to the chief pilot. In this case, I was assigned to fly with him because I was the most experienced F/O at the time.
We flew into LAX, and he was visibly nervous, intimidated by the size and business of the airport. When we departed, he was very hesitant in taxiing, seemed to be confused. On the takeoff roll we developed a door open light. It was relatively early in the takeoff, and I loudly announced the problem, pointed to the annunciator, and stated "Door light, reject, reject, reject." per the company SOP. No response. I stated again, and when I looked over at him, he was hunkered down, had a death grip on the yoke, one on the thrust levers, and showed no signs of doing anything but being intensely focused on taking off.
I knew a false door signal wasn't unheard of, and visually checked the door over my shoulder, and noted the handle positions. I determined that while clearly the door was closed, the indication didn't warrant trying to wrestle the airplane away from the captain who was off in la-la land and still apparently scared out of his whits. He wasn't unconscious, but more catatonic, overwhelmed from the look of it. I quickly determined a high speed rejected takeoff coupled with attempting to take control would do more harm than good.
When the captain didn't respond to further calls, but did rotate, I took care of gear and flaps. After we were cleaned up I tackled the checlist myself and then loudly anounced "You ARE aware we have a door light, correct?" He snapped out of it, and had a fit, stating that we needed to turn around, declare an emergency, and land the other way. He nearly had a panic attack. I left him physically manipulating the controls, but took control from that point on, telling him what to do, and talking him through the remainder of the trip.
When we got home I shared the experience with the Chief Pilot, who had grown to be good friends with that captain, and didn't want to hear it. I added my name to the list of pilots who wouldn't fly with him again, making it a full house; nobody would fly with that captain...and for the remainder of his time they called him a captain, and he was paid as a captain, but flew only with the chief pilot and only in the capacity of first officer.
I don't think the call is as simple as taking the airplane away, SOP notwithstanding. One must look at the circumstances and make the call.