Grapple rules seem to be geared towards a constant struggle between two or more combatants. But are there any rules around, say, throwing a wounded NPC over your shoulder to bring them to safety, picking up your party member's trio of pet rats, or having one of the creatures concede during a grapple? For example, what sort of action is it, and does doing so impose any sort of penalties?
Carrying a willing or unresisting creature is no different from carrying anything else.
As this answer explains, there aren't really rules for carrying creatures outside of a grapple (or Tiny/smaller creatures, which are already small enough to fit inside another creature's space). The rules for carrying someone in a grapple are pretty straightforward, though, as are those for carrying an object.
So, if I were DM, I'd present the character being carried with a choice:
They can choose to be passive; not attacking, not dodging, letting their carrier handle everything except maybe holding on. In this case they are treated as an object. Picking up something is a move action; picking up a "heavy" object also provokes attacks of opportunity.
While the carried character can't do anything, once they're picked up the carrying character doesn't have to spend any more actions on them and is free to act normally (with the usual encumbrance limits depending on their total load), though for a particularly heavy passenger (or one that can't hang on themselves because they're unconscious or something) I might say holding them requires one or both hands.
Attacks against the carried character are made using the sunder rules. Attacking them provokes an AoO just like sundering an object; this fits with the idea of the hero rescuing someone and driving people away from them with their weapon or something. Remove the AoO if the players abuse this too badly, but honestly I don't see it being a problem.
For the case of a grappling character surrendering, I'd also say it still takes a move action to get them into a convenient carrying position, same as above.
Or, the carried character can keep acting. Carrying someone moving around unpredictably, not in a natural position, and generally not going out of their way to make it easy to carry them is a lot trickier. Unless the carrier and/or the carried have some special training or ability making it easier (read "a feat, class feature, or something that provides its own specific rules") they're stuck using the grappling rules.
The SRD covers basically everything, but of special note is that moving a grappled character typically requires an opposed check. As DM, I'd probably say the carried character is taking 10 on the check, and not include their BAB in their grapple modifier (since they're not applying their skill towards actively resisting you).
As an additional note, you might be interested in the feats Fling Ally and Fling Enemy, both from Races of Stone. They do exactly what you'd expect, but do have some requirements. You have to be at least Large (or count as Large due to Powerful Build), have high STR, and be able to throw rocks due to either a racial ability or the Rock Hurling feat.