My friend put in an order of publication to adopt a child that is not his and he is no longer with the girlfriend and the Bio father is not in the child's life. Can my friend adopt the girls child if the child still lives with the mother and the mother is not giving up any parental rights and they are not together and how long will the process take and will the order of publication dismiss the Bio fathers parental rights so my friend can adopt?

Wait.

So your friend wants to adopt his EX girlfriend's child?

Very probably NOT going to happen. He needs to seek a lawyer to find out EXACTLY what his odds of doing so are.

I agree, its very unlikely to happen. Generally, courts look for a stable relationship before approving an adoption. This does not look stable at all.

Maybe the mother can list your friend as a godparent. While that doesn't give him any legal rights, its does make for a more formal relationship.