Here's how to drag an (string) item from a ListBox to an Edit control:

~~~~~~~~~~~~~~~~~~~~~~~~~
{
Set ListBox.DragMode = dmAutomatic
from the Object Inspector.

Let the OnDragOver and OnDragDrop
for the Edit control look like:
}

procedure TForm1.Edit1DragOver
  (Sender, Source: TObject;
  X,Y: Integer; State:TDragState;
  var Accept: Boolean) ;
begin
  Accept := True;
end;

procedure TForm1.Edit1DragDrop
  (Sender, Source: TObject; X,Y: Integer) ;
begin
  (Sender as TEdit).Text :=
    (Source as TListBox).Items
    [(Source as TListBox).ItemIndex]
end;

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Here are some more dragging and dropping related articles.

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