Although judges often say trial briefs are required the failure to file one would not usually prevent someone to put on a case. It is always better to file one, but it would not be as problematic as failing to file a list of witnesses or exhibits where that was required.
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The party is usually always allowed to testify but exhibits or witnesses may be excluded.
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Do not get over confident because Petitioner failed to file paperwork. The Petitioner can still testify. The standard is still "best interest of the child". If Petitioner does not show up for the trial most judges would give you almost all of what you're asking for. But, it is written into the code that it is normally in the best interests of the child to have frequent and continuing contact with both parents. So full custody that excludes time with the Petitioner is unlikely. A trial brief is not evidence, it is just a "road map" where you outline for the judge what you intend to prove at trial - you still have to prove it by proper evidence and testimony.
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