A recent Fox News story demonstrates the fact that in Colorado, genetic relatedness is not perfectly equivalent to paternity for custody and child support purposes (even in the absence of a legal adoption).
Paternity can be established in multiple ways in Colorado in addition to genetic relatedness, including through presumptions arising from marriage or birth certificates that sometimes become conclusive after a sufficient period of time, even if later found to be inconsistent with DNA evidence. There is also not perfect consistency between definitions of paternity under the law for different purposes (e.g. child support v. custody v. tax purposes v. Social Security v. immigration and nationality status v. inheritance).
Also, in Colorado, in addition to parents (and in some circumstances non-custodial grandparents), even completely unrelated persons who have lived with a child for at least six months in the six months before the proceeding, or with whom the child was present at the time that the proceeding was commenced, have standing to seek parenting time and parental responsibilities for the child on a equal footing with parents determined under one omnibus (and hopelessly vague) "best interests of the child" standard.
Apart from presumptions of paternity related to marriage of the mother of a child and some provisions related to inheritance, the law of child support and custody in Colorado is largely independent of the rest of divorce law. In other words, the rights of unmarried couples and married couples in child support and custody cases are basically the same.
It is also worth observing that merely having children together, or merely cohabiting (or both) even for decades, does not give rise to a common law marriage in Colorado (contrary to descriptions of common law spouses frequently made by law enforcement officers and journalists). Common law marriage in Colorado requires an agreement between two adults that they are married, that the couple hold itself out to the public as married, and (arguably) cohabitation or consummation. A common law marriage doesn't require years of cohabitation and once a couple is common law married, the bond cannot be broken except by divorce or death. There is no such thing as a common law divorce.
The main difference between married and unmarried couples that break up, legally, is that spouses may have claims to maintenance (a.k.a. alimony), responsibility for debts arising during the marriage on which a spouse may not otherwise be fully legally responsible, and a right to equitable division of property acquired during the marriage even if titled in the other spouse's name.
In contrast, a partner in an unmarried couple with children is typically entitled to child support and custody of the children, but not to any additional maintenance, to assistance from the other partner with debts in the unmarried partner's name, or to property that is titled or legally owned by the other partner.
(There are also marital rights related, for example, to wrongful death lawsuits, inheritance, Social Security benefits, taxes, and decision making related to a partner who can not make decisions for him or herself.)