We have replaced a lot of K&T over the years and seen a lot but this one takes the cake. The initial call was from smoke coming out of the closet ceiling. While we did not find a smoking gun when we first arrived (it was the next day after the reported smoke) we did notice the 14 gauge K&T was divided into three circuits all on the same 14 gauge neutral and all from the same 120 volt fuse box. So all three circuits were on the same leg of the service (*actually 4 if you count the door bell transformer). Of course all four fuses were the usual 30 amp ones that we normally see. My theory is that the neutral got mighty hot and that is what was making the smoke. Two days of rewiring and we haven't found anything visibly burnt in the attic.
K&T is basically air cooled so it will handle more current than any cable or raceway wiring method although you still use the same ampacity charts. I imagine the smoke was just the dust burning off the conductors, similar to the first time you turn on the toaster wire heat strips in an air handler after a long time. Here in SW Florida it might be years since the last time you had the heat on. Were any of the conductors discolored?
That's somewhat common in bodged wiring upgrades in central Europe. Cookers (ranges) usually have the elements connected L-N but take three phases to spread the load, either on a 3-pole 16 amp or three single poles. Two hob elements per phase and the oven on the third (it's rare to see anything with more than four elements and a single oven here, the typical load is 6.5-8 kW). However, if the incoming mains is only single-phase 2w but the installer sets up the cooker circuit for three-phase 4w, the neutral could see up to 3x16 amps. In Austria that's somewhat de-fused by the typical 25 amp limit on the incomer but in Germany the incomer could be fused at up to 63 amps.
I've seen that once or twice in Austria but decided to leave it - 2.5 mm2 and a 25 amp bottle fuse is marginal because of the slower overload trip of the fuse compared to a B/C MCB but unlikely to burn the house down and it was decidedly temporary - the installer had put back the original single-phase meter, jumpering all the load-side lives until the grid operator's subcontractor installed the new three-phase meter. Usually that shouldn't take more than a few days but in this instance it was about two months.