Pinktwink's answer might not apply. It depends upon when your child was born.
Your ex-partner has automatic parental responsibility if either:
(a) he was married to you when your child was born ; or
(b) your child was born on, or after, 1st December 2003 and (as you state) his name appears on the child's birth certificate.
If your child was born before 1st December 2003 (and you were not married to your partner when the child was born), your ex-partner will not have parental responsibility unless either
(a) you have voluntarily entered into a formal agreement giving him parental responsibility ; or
(b) he has sought, and obtained, a parental responsibility order from a court.
Your partner moving away makes no difference as to whether he has parental responsibility or not. If he currently does not have parental responsibility he can still apply for it but it would not be granted automatically. The court would take the following into account:
* the degree of commitment shown by the father to his child
* the degree of attachment between father and child
* the father's reasons for applying for the order
http://www.direct.gov.uk/en/Parents/ParentsRig hts/DG_4002954
Chris