Your friend's ex can only prevent her taking their son out of the country if he has obtained parental responsibility. These are the four ways in which he could have parental responsibility:
1. You make no mention of marriage but (for the sake of completeness) I'll mention that the ex would have automatic parental responsibility if he had been married to your friend at the time of the child's birth (irrespective of whether his name appeared on the birth certificate) ;
2. As your post implies, the ex would have parental if he had jointly registered the child's birth along with your friend (i.e. if his name appeared on the birth certificate) ;
3. The ex could also obtain responsibility through your friend voluntarily entering into a formal parental responsibility agreement with him (which seems to be an unlikely scenario).
Lastly . .
4. The ex could apply to a court to seek parental responsibility. The court would have to consider the degree of commitment shown by the father to his child, the degree of attachment between father and child, and the father's reasons for applying for the order (which could include his fear that the child would be permanently taken out of the country).
Relevant links:
http://www.direct.gov...entsRights/DG_4002954
and
http://www.direct.gov...ildpassport/DG_174106
Chris