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The count of the MDIChild forms can be looked in the MDIChildCount property. In this example you can open 10 MDIChild forms only. Don't forget to remove line Application.CreateForm(TForm2, Form2) from project file and line var Form2: TForm2 from unit2.pas file.

procedure TForm1.New1Click(Sender: TObject);
var
  ChildForm: TForm2;
begin
  if MDIChildCount