Some monsters are capable of dividing into two new monsters of the same type. The type of division depends on the type of monster involved.
Gremlins, brown molds, and blue jellies can divide into two with half the HP and maximum HP of the original - the former from any source of water and the latter two from inflicting damage with their passive cold attacks.
Brown and black puddings will divide into two with half the current HP but the same maximum HP as the original monster when hit with any iron item. As the maximum HP does not decrease, it is possible to split these monsters indefinitely if they are healed after splitting, giving rise to the practice of pudding farming. (As of NetHack 3.6.0, puddings and molds no longer leave corpses, making farming inviable.)