function FillNetLevel(xxx: PNetResource; list: TStrings): Word;
type
  PNRArr = ^TNRArr;
  TNRArr = array[0..59] of TNetResource;
var
  x: PNRArr;
  tnr: TNetResource;
  I: integer;
  EntrReq,
    SizeReq,
    twx: Integer;
  WSName: string;
begin
  Result := WNetOpenEnum(RESOURCE_GLOBALNET, RESOURCETYPE_ANY,
    RESOURCEUSAGE_CONTAINER, xxx, twx);
  if Result = ERROR_NO_NETWORK then
    Exit;
  if Result = NO_ERROR then
  begin
    New(x);
    EntrReq := 1;
    SizeReq := SizeOf(TNetResource) * 59;
    while (twx < > 0) and
      (WNetEnumResource(twx, EntrReq, x, SizeReq) <> ERROR_NO_MORE_ITEMS) do
    begin
      for i := 0 to EntrReq - 1 do
      begin
        Move(x^[i], tnr, SizeOf(tnr));
        case tnr.dwDisplayType of
          RESOURCEDISPLAYTYPE_DOMAIN:
            begin
              if tnr.lpRemoteName < > '' then
                WSName := tnr.lpRemoteName
              else
                WSName := tnr.lpComment;
              list.Add(WSName);
            end;
        else
          FillNetLevel(@tnr, list);
        end;
      end;
    end;
    Dispose(x);
    WNetCloseEnum(twx);
  end;
end;

Итак, слегка подправленный вариант. На форме находится Button и RichEdit

unit Unit1;

interface

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

type
  TForm1 = class(TForm)
    Button1: TButton;
    RichEdit1: TRichEdit;
    procedure Button1Click(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;
  Res: TNetResource;
  s: TStrings;
implementation

{$R *.dfm}

// Переменная List заполняется списком доменов.
// Функция возвращает код ошибки обращения к сети.

function FillNetLevel(xxx: PNetResource; list: TStrings): Word;
type
  PNRArr = ^TNRArr;
  TNRArr = array[0..59] of TNetResource;
var
  x: PNRArr;
  tnr: TNetResource;
  I: integer;
  EntrReq,
    SizeReq,
    twx: THandle;
  WSName: string;
begin
  Result := WNetOpenEnum(RESOURCE_GLOBALNET, RESOURCETYPE_ANY,
    RESOURCEUSAGE_CONTAINER, xxx, twx);
  if Result = ERROR_NO_NETWORK then
    Exit;
  if Result = NO_ERROR then
  begin
    New(x);
    EntrReq := 1;
    SizeReq := SizeOf(TNetResource) * 59;
    while (twx <> 0) and
      (WNetEnumResource(twx, EntrReq, x, SizeReq) <>
      ERROR_NO_MORE_ITEMS) do
    begin
      for i := 0 to EntrReq - 1 do
      begin
        Move(x^[i], tnr, SizeOf(tnr));
        case tnr.dwDisplayType of
          RESOURCEDISPLAYTYPE_DOMAIN:
            begin
              if tnr.lpRemoteName <> '' then
                WSName := tnr.lpRemoteName
              else
                WSName := tnr.lpComment;
              list.Add(WSName);
            end;
        else
          FillNetLevel(@tnr, list);
        end;
      end;
    end;
    Dispose(x);
    WNetCloseEnum(twx);
  end;
end;

procedure TForm1.Button1Click(Sender: TObject);
begin
  try
    s := TStringList.Create;
    FillNetLevel(@Res, S);
    RichEdit1.Lines.Assign(s);
    S.Free
  except
    S.Free;
    ShowMessage('Не удалось получить список доменов')
  end
end;

end.