If the parents are not married at the time of the child's birth, then the mother retains all custodial and other rights unless or until the father establishes such rights according to Ga law, through a combination of the following: marriage after birth, signing of Voluntary Acknow. of Paternity and/or Legitimation, and/or court order (which would establish custody and visitation for father). As child support is automatically required of both parents at the time of conception, a court could enforce that right of the child if necessary under the circumstances.
In terms of death, assuming the parties were not married at the time of birth of the child, the father would not have any automatic custodial rights. If the father sought to establish said rights after the death of the mother, he would have to go to court to establish paternity, legitimation, and custody. While a testamentary guardianship (whether guardianship in a natural guardian such as a parent or a 3rd party) would be presumed by the probate court, absent evidence to the contrary, ultimately, it is up to a court, whether probate, juvenile, and/or superior (depending on the facts and circumstances of the particular case), to determine who the child should reside with (esp. in the absence of a natural legal parent), based on the "best interest of the child" standard.
As I assume you are the mother of the child you speak of, I strongly advise that you make a good and thorough will quickly, and if you don't want your child's father to be presumed to be the likely candidate (obviously after he accomplishes what I previously discussed herein), you should include in the will a provision stating who you desire to be the testamentary guardian (e.g., a close trusted relative, or close friend). Also, any property that you have at your death, if not in the father's name, and which you can dispose of as you desire, you can place in the name of your child, to be held in a trust until a certain age (e.g., at least 18 yrs old, or some other time in the future). While a basic trust is not necessarily complicated to set up, there are plenty of good professional estate planners and estate/trust attorneys who can assist with that. Good luck.
The father could get custody, if he already legitimized the child, or if he makes certain filings now. A grandmother could also seek custody. If the mother left a will that made a choice of guardian, a court must consider it, but could elect not to follow it. This is a situation where you need a lawyer IMMEDIATELY.
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I am assuming that the mother and father are not married and never were married. If that is the case, the father is not legally the father. He is referred to as a "stranger to the child". The father may file a petition for legitimation in the county where the chid is found. If no one contests his petition, he will probably succeed in establishing his rights as the child's parent and obtain physical custody.
However, if the deceased's parents (or other persons with a family relationship) intervene for custody, the court will have to decide whether it is substantially better for the child to be placed with a family member other than the father. This decision will require the court to examine many factors. For example, the court will probably want to know about the capacity of the father to support the child, any criminal record, etc.
Since the parents were not married at the time of the birth of the child, the child is considered to be born out of wedlock and therefore illegitimate. A father of an illegitimate child has no custody rights until he legitimate the child and obtains a court ordered award of custody. In this particular situation, I would strongly recommend that the survivors and closest relatives to the mother obtain the advice of an experienced family law attorney for more information. The mother's relatives may be in a position to seek custody of the child. At a minimum, the child probably would be considered a "deprived child" under Georgia law, which means that a surviving relative could petition the juvenile court in the county where the child is currently living to get custody. However, that is a complicated process, and that could be the wrong answer for you at this time. You need to speak with an experienced custody lawyer for more information. I would caution you against trying to do this on your own.
Nothing contained herein shall be considered or construed as creating an attorney client relationship between the party asking the question and the attorney. All legal problems are different. The answer given is only a general response based upon the facts provided and should not be considered specific advice for your case. Always contact a lawyer for advice about your particular circumstances and issues. For additional information, you may wish to view our firm website at www.pbcl-law.com. Our firm can assist with custody, child support, divorce, contempt, separation, and other family law matters in Cobb, Fulton, Dekalb, Forsyth, Paulding, Douglas, Bartow, Cherokee, Gwinnett, and other counties in the Atlanta Metro area.