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When a child is born to unmarried parents, paternity
has to be established before the father has the ability to assert any parental rights
. Ore. Rev. Stat., Section 109.103. You also have to establish paternity before you can seek the support that your child is legally entitled to (even if you don't want it, you can stick it in the bank and give it to the child when they're an adult or use it for college or something).
The state can help you get a child support
order and collect the money for you if you apply for services.
Until you go to court to get a custody order, you do have sole custody. You wouldn't have any obligation to let him take the baby or spend any time with the baby without a custody order. When you apply through the state, they're just doing support, not custody. You'll still be the custodial parent
If the father did seek custody or visitation
, the judge would consider all of his prior behavior when determining whether it's best for the child to spend time with him. You could ask that he get help for his alcoholism
before being allowed to take the baby home. That's a fairly common request and would likely be granted. If he's not making any real effort to get to know his daughter after 4 months, and pays $0 in support, that will also count against him.
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