Paedophilia
From wipipedia.org

Paedophilia or pedophilia is a sexual desire directed towards children. The diagnostic criteria for pedophilia are:
- A. Over a period of at least 6 months, recurrent, intense sexually arousing fantasies, sexual urges, or behaviours involving sexual activity with a prepubescent child or children (generally age 13 years or younger).
- B. The fantasies, sexual urges, or behaviours cause clinically significant distress or impairment in social, occupational, or other important areas of functioning.
- C. The person is at least age 16 years and at least 5 years older than the child or children in Criterion A.
Note: it is NOT required that the person have ever acted on their urges in order for them to be a paedophile (which means literally "love for a child"). The correct term for someone actually engaging in sexual relations with a child is Pederast.