Petition for (Custody) (Visitation). The forms below are some of the most common forms used in the Domestic Relations Division, but there are many more.This document provides an overview of the basic steps to file for custody of a child in Cook County,. Illinois. To fill out the Supplemental. Petition, start at the top and fill in the blanks. Download and complete Divorce, Child Support, and Maintenance forms from the Illinois Office of the Courts. Use this form to ask the judge to give you parental responsibilities for a child. This includes parenting time (visitation) and decision-making power (custody). Child Custody Evaluations; Children and Teens Speak. Use this form to ask the judge to give you parental responsibilities for a child.