No, the Judge will not "automatically" issue an order of alternate weekend visitation. That's because every case is different - and plays out differently. One can only say that's the "average" visitation order for a non-custodial parent (and usually a mid-week dinner visit as well), but it's hard to predict what exactly will happen in your case. That said, you're highly encouraged to schedule a consultation with a Bronx Child Custody attorney.
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From what you say, unless you are unrepresented in court, there is the high probability that the court will maintain the established relationship you descirbe.
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