Asimina triloba, the American pawpaw. is a species of Asimina in the same plant family (the Annonaceae) as the custard-apple. understory tree. a large shrub or small tree growing to a height of 11 m with a trunk 20–30 cm or more in diameter. Pawpaw fruits have a sweet, custardish flavor somewhat similar to banana, mango, and cantaloupe. The natural insecticides in the leaves, twigs, and bark of pawpaw trees can be used to make an organic pesticide.