When you talk about the object's "child", there are two possible interpretations:
1) The object is a TComponent and Owner of your children, which can be accessed by the Components property. For example:
for i := 0 to Form1.ComponentCount - 1 do
if Form1.Components[i] is TLabel then
TLabel(Form1.Components[i]).Caption := IntToStr(i);
2) The object is a TControl and Parent of your children, which can be accessed by the Controls property. For example:
for i := 0 to Panel1.ControlCount - 1 do
if Panel1.Controls[i] is TLable then
TLabel(Panel1.Controls[i]).Caption := IntToStr(i);
Generally the Form is the Owner of all components and visual controls that contain other controls (when the parent moves the children go together) are the Parents of their children.