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Even if he’s not involved because he is on birth certificate he has parental rights regardless of baby’s last name. I read an article about it the other day, I’ll see if I can find it for you (it was written by a lawyer).
https://www.mybump2baby.com/travelling-with-your-child-after-separation-the-dos-and-donts/
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If surname matches yours it be fine. If different you need get the letter of consent etc done He may stop you tho but if he doesn’t the airport would let u go