Wikipedia says
you're done: Quote:
Genitalia
A boy's penis grows little from the fourth year of life until puberty. After the penile growth of early infancy the average childhood penile length is about 7 cm. The prepubertal genitalia are described as stage 1. Within months after growth of the testes begins, rising levels of testosterone promote growth of the penis and scrotum. This earliest discernible beginning of pubertal growth of the genitalia is referred to as stage 2. The penis continues to grow until about 18 years of age, reaching an average adult size of about 10-16 cm[citation needed].
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And yes, ofcourse there is a genetic link. You inherit pretty much everything from your parents.