Medieval illustrations sometimes depict horsemen who have tilted their great helms off their head in order to get better vision, hearing, ventilation, recognition, or whatever; the helm usually ends up sticking out perpendicularly from the back of the wearer's neck in this situation. My question is: how were those helms attached so that they wouldn't pull on the hauberk/surcoat and choke the wearer? Is it just a matter of attaching the helm to the usual chains on the wearer's chest and making sure that the chest-piece that the chains are attached to (hauberk, surcoat, CoP, placket, whatever?) is snug enough that it wouldn't ride up towards the wearer's neck? Or is it something else entirely?

I don't know the factual answer. (I have not read any period text describing this exactly.) My expectation is that a piece of leather cord would have tied it off to the neck area of the mail. I would not expect it to wrap around the wearer's throat and cause that kind of obvious hazard. I believe one of the previous posts here on crested helms with horns shows a great helm dangling from what appears to be a cord.

Leather thongs were used a lot with late 12th to 13th century era mail; Baggy areas of mail were "tightened up" and better secured at points on arms and legs by binding it with leather lace. Backs of chauses were laced shut with thongs, etc. At the mid point of the high frequency tournament era (turn of 12th to 13th century), it was even described in period texts as fashionable to leave the excess ends of the thongs extra long with some knots in them so that the thongs would crack like whips while entering joust opponents made fast dashes down the lanes on their horses just to impress the crowd..