Regarding the training of potty use

The discovery that one's very small child has decided to potty train themselves seems at first to be an optimal situation. That delusion lasts about as long as it takes to clean up the first floor puddle. Of course a child this small simply cannot be convinced by any reasonable parent that they, in fact, are not potty trained. The attempt to re-dress the leaky areas of said child's anatomy is met with rather disruptive and eruptive denial. The attempt to direct said child toward the loo before leakage occurs is met with the same. What, then, should one do if they are saddled with a leaking child who insists on sitting on the toilet for 1/2 hour before hopping off and promptly relieving themselves on the floor? My simplistic response is as follows; prepare the coffee early, cover irreplaceable and stainable furniture (if you have more that one child you are smart enough to have given these away by now) and have hand towels at the ready in every room. If this does not protect some semblance of sanity then I am not certain sanity has any hope of being saved.