Do you have an attorney? If you do, ask this question to that person. Was the support paid pursuant to a court order? If so, he could be held in contempt of court. Sole custody is not favored and is only allowable under certain circumstances.
First and foremost, if you were never married to the father, and there is not court order giving him shared parental responsibility or any timesharing, then you already have sole parental resposibility and 100% timesharing under Florida law. Florida Statute §744.301(1) states “the mother of a child born out of wedlock is the natural guardian of the child and is entitled to primary residential care and custody of the child unless a court of competent jurisdiction enters an order stating otherwise”.
Furthermore, Florida Statute 742.031 (2) states “if a judgment of paternity contains only a child support award with no parenting plan or time-sharing schedule, the oblige parent shall receive all of the time sharing and sole parental responsibility without prejudice to the obligor parent. If a paternity judgment contains no such provisions, the mother shall be presumed to have all of the time-sharing and sole parental responsibility.”
If the Father has been granted parental responsibility you can petition the Court to terminate his parental rights. Florida Statute § 39.806 states that the court can terminate a parents rights if they have abandoned the child.
Florida Statute §39.01 states "“Abandoned” or “abandonment” means a situation in which the parent or legal custodian of a child or, in the absence of a parent or legal custodian, the caregiver, while being able, makes no provision for the child’s support and has failed to establish or maintain a substantial and positive relationship with the child. For purposes of this subsection, “establish or maintain a substantial and positive relationship” includes, but is not limited to, frequent and regular contact with the child through frequent and regular visitation or frequent and regular communication to or with the child, and the exercise of parental rights and responsibilities. Marginal efforts and incidental or token visits or communications are not sufficient to establish or maintain a substantial and positive relationship with a child. The term does not include a surrendered newborn infant as described in s. 383.50, a “child in need of services” as defined in chapter 984, or a “family in need of services” as defined in chapter 984. The incarceration of a parent, legal custodian, or caregiver responsible for a child’s welfare may support a finding of abandonment.
This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice nor does it constitute an attorney-client relationship
In order to properly answer your question, you should speak with an experienced family law attorney, and "fill in the gaps" that exist in your question. Specifically, do you have an Order from a court that is awarding the support payments he was making? If so, was it entered as a part of dissolution of marriage proceedings, or a proceeding specifically for child support? Was there a parenting plan that was created along with the award of child support, and if so, what does the parenting plan say regarding timesharing with the child? Was the child born outside of marriage?
Your question requires that all of these questions be answered, and that an attorney review the Order in which the Court awarded child support, if one exists.
As an aside, there is no longer the concept of "custody" in Florida. Florida now uses a concept known as parental responsibility, and there is a statutory assumption that both parents should have equal input to decision making and access to a child. This is unless the parties agree otherwise, or a Court orders otherwise. Sole parental responsibility (which replaces the concept of "full custody") is an extremely difficult goal to achieve, and there must be compelling evidence before a Court that sole parental responsibility is in the best interests of the child.
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