I am 100% sure that if I broke up with my girlfriend or boyfriend, I would not need to sign any official documents. As far as I know, the procedure if we were married instead would be a bit more complicated (because of the involvement of the State).

If it were a "romantic way of expressing one's commitment to another person," it would be enough to throw a party with friends, read a couple of fashionable poems, sign a guest book instead of an official register, and not invite the State into private affairs.