When do i become residental parent?

my wife left me months ago she left the children with me she has only seen the children twice my question s because she left me with children is there a certain amount of days when I t com residential parent because they live with me and I give me more rights than she has when it comes to decisions about there well being also do I have the right to file for child support ? I will be in the state of ohio I have a children 2 an 3 years old