AAA = class(TObject)
         ...........................
         ...........................        
     public 
         B: Thread;
         procudure  ExecuteMyObject; 

     constructor AAA.Create((..............)
     begin 
         B:=Thread.Create(False);
         B.Execute :=  ExecuteMyObject;   ????????????
        ///Здесь не понимаю как пойдет процесс присвоения и дальнейшей вызов. 
     end;

     procudure  ExecuteMyObject; 
     begin 
        /// основной функционал для выполнения в потоке ... 
     end;

type
  TAddSpan = class;

  TAddExec = class(TThread)   //поле основного объекта
  private
    Parent: TAddSpan;
  protected
    //
  public
    constructor Create(aParent: TAddSpan);
    procedure   Execute; override;
  published
    //
  end;

  TAddSpan = class(TObject)   
  private
    thExec:   TAddExec;
 protected
    //
 public
    ......................
    procedure   ExecuteThread;
    procedure   ExecuteParent;
  published
    //
  end;

implementation

uses Main;

  constructor TAddExec.Create(aParent: TAddSpan);
  begin
    Parent:=aParent;
    Inherited Create(True);
  end;

  procedure TAddExec.Execute;
  begin
    Parent.ExecuteParent;
  end;


  procedure TAddSpan.ExecuteThread;
  begin
    thExec:=TAddExec.Create(Self);
    thExec.Resume;
  end;

  procedure TAddSpan.ExecuteParent;
  var I: Integer;
      L: TStringList;
  begin
    L:=TStringList.Create;
    for i:=1 to 20000000 do begin
      L.Add('Row '+IntToStr(I));
    end;
    L.SaveToFile('C:\WORK\rr12.txt');
    L.Free;
  end;

type
  TTaskProc=procedure (Sender:TWrkThread;Param:pointer);
  TTaskProcObj=procedure (Sender:TWrkThread;Param:pointer) of object;

type
  TMethod  = procedure of object;

  TAddExec = class(TThread)
  private
    ParentExecute: TMethod;
  protected
    //
  public
    constructor Create(aMethod: TMethod);
    procedure   Execute; override;
  published
    //
  end;


implementation

uses Main;

  constructor TAddExec.Create(aMethod: TMethod);
  begin
    Inherited Create(True);
    ParentExecute:=aMethod;
    FreeOnTerminate:=True;
    OnTerminate:=frMain.TerminateThread;
  end;

  procedure TAddExec.Execute;
  begin
    ParentExecute;
  end;

 ..................
 ..................
 ..................
 ..................

  procedure TAddSpan.ExecuteThread;
  begin
    thExec:=TAddExec.Create(Self.Execute);
    thExec.Resume;
  end;