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How exactly is this different exactly from Parents for a Day? I don't see any differences at first glance.
It's not explicit, but it's implied that Parents for a Day is where the childcare IS the plot, whereas Babysitting Episode is where the character(s) have to deal with the plot WHILE watching a kid. I agree though that it's awfully fuzzy and doesn't really need to be two different tropes.
EDIT: Also, Parents for a Day appears to be children only, while Babysitting Episode can include senile elderly and pets/animals.
With that said, I have no idea which page to add the Samurai Jack example to.
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How well does it match the trope?