type
  TFormMDIChild = class(TForm)
    procedure FormClose(Sender: TObject; var Action: TCloseAction);
  private
    FFrame: TFrameBase;
    procedure SetFrame(const Value: TFrameBase);
    { Private declarations }
  public
    property Frame: TFrameBase read FFrame write SetFrame;
    { Public declarations }
  end;

implementation

{$R *.dfm}

{ TFormMDIChild }

procedure TFormMDIChild.FormClose(Sender: TObject; var Action: TCloseAction);
begin
  Action := caFree;
end;

procedure TFormMDIChild.SetFrame(const Value: TFrameBase);
begin
  FFrame := Value;
  if FFrame <> nil then
  begin
    FFrame.Parent := Self;
    FFrame.Align := alClient;
  end;
end;

....
  // А потом что-то вроде
  TFormMDIChild.Create(Self).Frame := TMyFrame.Create(Self);