Your child being born out of wedlock will make no difference to the Court establishing shared parental responsibility and time sharing with the child. Primary custody to provide the child's residence will be based upon what will be in the child's best interests.
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When the parents of a child born out of wedlock marry after the birth of the child, the child becomes legitimized. See Florida Statute 742.091 which states in apart:
"If the mother of any child born out of wedlock and the reputed father shall at any time after its birth intermarry, the child shall in all respects be deemed and held to be the child of the husband and wife, as though born within wedlock,. . ."
As such, the parents would have equal rights to the child.