I've never trained with a partner, and I don't use a spotter unless someone offers. That's only because every set, I go to failure.... (or the rep before failure). One set is okay if someone is resting between sets themselves, but I don't feel right calling them over again and again.
However, I've noticed that I always break my records when someone is there spotting. I guess you always wanna appear stronger to whoever is watching.
Anyway, I usually rep to the point where I'm struggling to get it up.... usually takes about 5 seconds to complete the concentric contraction, and I know one more rep will be absolute failure and I'll get squished.
A few times I overestimated how much steam I had, and just couldn't make it. At the gym I'm at now, they have the rack things down near the sticking point as well, so that's saved me a few times. But once or twice I've had to roll the bar down my chest and stomach, and sit up.... luckily I was young and not lifting any huge amount.