You should really consult with an experienced family law attorney in your area. Having said this, despite the distance, the father may have visitation rights and or some custodial rights despite the move. It depends on several factors and facts which only a thorough consultation would reveal. Most likely, you would be awarded a majority time share with your child, but not for certain. Nothing is certain in family law court until there is a judge's decision made. Furthermore, there are two types of custody - physical custody (where the child stays) and legal custody (decision-making powers of the respective parties). So, that's another area that you'll need to discuss with a lawyer. Best of luck to you and your child.
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If the party lives over 100 miles away and is not involved you have defacto sole custody. Why go to court and risk a different order? Just keep a calendar of the dates and times he visits. Don't go to war when there is nothing to win.
213-819-1171 Please only call me if your case is in California as I am only licensed here and laws of other states may vary. I approach trials and issues from a legal and common sense approach, This is how the majority of judges I have appeared before in 40 years also make decisions. I do not intend by my advice to enter an attorney client relationship and in most cases advise to obtain legal representation. Sometimes if you can not afford it a consultation or limited scope representation is available. As an experienced attorney I can tell you, judges can be impatient, hate emotional arguments and over exagerations or lies. A brief outline of the problems and desired solutions is always best and I often in limited scope representations advise clients on how to proceed at time of hearing or trial and my fees are considerably less when I do not appear in court as it takes much less of my time.
This question is challenging without additional information, however...
If there is a current custody judgment granting either sole legal or joint legal custody, there will likely need to be a significant change of circumstances to alter that previous judgment.
If there is a current custody order either granting sole legal or joint legal custody, the burden to change will be either a significant change of circumstances or the best interest of the child depending on whether the order was permanent or temporary (modification of permanent orders requires the higher burden of significant change of circumstances).
If there is no custody order or judgment then it depends on what Father's position on the matter is. I will assume he would like to have joint legal custody since you are asking the question. If that is the case, the court will inquire as to the minor child's age (to see how long father has been absent), the court will inquire as to the reason behind father's absence and the court will inquire as to the reasoning behind each party's position.
In general, the court defaults to shared or joint legal custody. However, if there are co-parenting problems and the child is primarily with you then you can request that you have decision making powers should both you and Father disagree on any legal matter regarding your minor child.