Papa Drop is extremely stubborn and unreasonable, berating or abusing anyone who disagrees with him or does not obey his orders and he even goes as far as attempting to interrogate Dot while she is gagged. When he interrogates Dot properly, he and his troops constantly accuse her of lying to them even though she is innocent and not even from their planet until finally he has Dot sent to the 'Prison for Squares' and Dot insults him and his troops.
Papa Drop has a son named "Roley" (aka "The Party"), whom he forbids to even see his love interest, a Squarey named Poley, and abuses Roley so much that Roley goes under-cover as a means of defying his cruel father.
Papa Drop always makes Squareys do hard labor and when his son brings food, it's always bad soup. Papa Drop always deflates when he loses his temper, but he is always inflated back by an inflator named Inflato. This is instrumental in his own eventual defeat, when he is inflated so much that he floats away, his troops and people having finally realized what a fraud he is thanks to Dot and The Party.
Like all of the male characters in the film, Papa Drop is voiced by Keith Scott.