You and your girlfriend have absolutely nothing to worry about. The legal principles I stated above come directly from Oregon case law, i.e., the way Oregon Courts have interpreted Oregon Custody Laws in actual custody cases and they state:
"...If the parents are not married, but paternity has been established either by signatures on the birth certificate or in a lawsuit, custody might have been granted by the law to the child's mother, if she is the physical caretaker, even in the absence of a Court Order.
So, your girlfriend, being the primary caregiver, is presumed by law to have legal custody of her son. This means that if the child's father decides to be malicious and vindictive, calls the police and alleges that the mother is going to kidnap the child, or take him out of state, the police cannot do anything to help him and can do nothing to prevent your girlfiend from coming to visit you.
In the absence of a Court Order giving him visitation or partial custody, the Courts have consistently held that father has no custody or parenting time rights, despite his name appearing on the birth certificate.
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