The small black tube from the ballcock to the overflow tube
does the refilling of the bowl after the flush.

This AmStd Champion model is a modern design; no ballcock. Mine was
put into service in OCTober 2005. The lift chain had fallen away and
I reinstalled that to get the toilet to flush again, but perhaps the
tube should be pointed into the overflow tube ? It is now discharging
into the tank.


There's your problem. The small plastic tube should discharge right into the
overflow standpipe. Often there is a small holder built into the top of the
standpipe to hold the fill tube, but it might have a clip.

Dennis