All without atmospheres?? . . . . ever?? Lightening in the wild tens to start small and all the fans end up contributing to a fat trunk. The fans could start at the very tops of the clouds as static between water molecules that might still be liquid rather than frozen. That would be similar to 'horizontal lightening' so 'the trunk' would start where the horizontal turned 'vertical'.
The barely hardened crust and the material we now call the crust was in friction with the top of the mantle and that would cause static electricity to be present. Volcanoes have lightening, carpets and sock and door-knobs are when all the little parts follow a single path (of least resistance). It is enough that a person will shake their finger from pain. In Canada's north those locations could where the diamonds will be found in a 'sea of damn hard rock'. When we last covered this I hinted that the biggest discharges would have been between the core and the inner-core to the point it vaporized the heaviest parts of the earth. The heat the earth sheds into space is keeping that process in check. I'm going to go with a little ice being a lot better than those areas being boiling water.
Using Hudson Bay as one of those 'fat trunks' the 'rivers' that drain into it would be following the path laid out when it was still a liquid.Those fans are depressions, all material above them is lighter and the original pattern is repeated rather than filled in flat like Sask was as the ice moved back and forth. If it does that in one place it cannot dig big holes like the Great Lakes. A map that looks like a spider web would be the one you want to be looking at. Some lakes should drain a large area and have no outlet.