All in all we are talking about company procedures here. So every company will do them quite differently. As explained above we do not even note deicing in our TLB at all. Nor did we hand out copies of the last TLB page out to ramp agents for quite a few years, we just recently restarted it after a five or six year break. Since TLB entries enroute or away from base are also done via ACARS, everything is electronically documented anyway, no need for paper really.
Additionally on most airports we have on our route network there is no direct paper trail at all, as deicing requests are coordinated via VHF and not with a form.