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Answer:

unit Unit1;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls, ExtCtrls;

type
  TForm1 = class(TForm)
    Timer1: TTimer;
    Memo1: TMemo;
    procedure FormCreate(Sender: TObject);
    procedure Timer1Timer(Sender: TObject);
  private
    { Private declarations }
    FAnchors: TAnchors;
    procedure WMMOVING(var Msg: TMessage); message WM_MOVING;
  public
    { Public declarations }
  end;

var
  Form1: TForm1;

implementation

{$R *.dfm}

uses Math;

procedure TForm1.WMMOVING(var Msg: TMessage);
begin
  inherited;
  with PRect(Msg.LParam)^ do
  begin
    Left := Min(Max(0, Left), Screen.Width - Width);
    Top := Min(Max(0, Top), Screen.Height - Height);
    Right := Min(Max(Width, Right), Screen.Width);
    Bottom := Min(Max(Height, Bottom), Screen.Height);
    FAnchors := [];
    if Left = 0 then
      Include(FAnchors, akLeft);
    if Right = Screen.Width then
      Include(FAnchors, akRight);
    if Top = 0 then
      Include(FAnchors, akTop);
    if Bottom = Screen.Height then
      Include(FAnchors, akBottom);
    Timer1.Enabled := FAnchors <> [];
  end;
end;

procedure TForm1.FormCreate(Sender: TObject);
begin
  Timer1.Enabled := False;
  Timer1.Interval := 200;
  FormStyle := fsStayOnTop;
end;

procedure TForm1.Timer1Timer(Sender: TObject);
const
  cOffset = 2;
var
  vHandle: THandle;
begin
  vHandle := WindowFromPoint(Mouse.CursorPos);
  while (vHandle <> 0) and (vHandle <> Handle) do
    vHandle := GetParent(vHandle);
  if vHandle = Handle then
  begin
    if akLeft in FAnchors then
      Left := 0;
    if akTop in FAnchors then
      Top := 0;
    if akRight in FAnchors then
      Left := Screen.Width - Width;
    if akBottom in FAnchors then
      Top := Screen.Height - Height;
  end
  else
  begin
    if akLeft in FAnchors then
      Left := -Width + cOffset;
    if akTop in FAnchors then
      Top := -Height + cOffset;
    if akRight in FAnchors then
      Left := Screen.Width - cOffset;
    if akBottom in FAnchors then
      Top := Screen.Height - cOffset;
  end;
end;

end.