When does penis growth stop?

After puberty. There is usually a fairly rapid period of growth of the penis itself which occurs during puberty. One of the first steps of puberty is the growth of the testicles which get bigger to accomodate all of the hormonal changes they are meant to support. These hormonal changes include growth of the penis itself. Penile growth outside of this usually stops at the end of regular growth between 15-20.
19. Specific time varies between people but it usually stop around the age of 19. After this size will slowly decrease over the following decades.