for i := 0 to SomePageControl.PageCount - 1 do
SomePageControl.Pages[i].TabVisible := false;

pc.Style := tsButtons; // или tsFlatButtons

unit MyPageControl;
interface
uses
 SysUtils, Classes, Controls, ComCtrls, Types;

type
 TMyPageControl = class(TPageControl)
 private
   FHideTabs: boolean;
   procedure SetHideTabs(const Value: boolean);
   { Private declarations }
 protected
   procedure AdjustClientRect(var Rect: TRect); override;
 public
   { Public declarations }
   constructor Create(AOwner: TComponent); override;
 published
   { Published declarations }
   property HideTabs : boolean read FHideTabs write SetHideTabs default false;
   property Color;
   property ParentColor;
 end;

procedure Register;

implementation
procedure Register;
begin
 RegisterComponents('MyComponents', [TMyPageControl]);
end;

{ TMyPageControl }

procedure TMyPageControl.AdjustClientRect(var Rect: TRect);
begin
 inherited;
 if HideTabs and not (csDesigning in ComponentState) then
   begin
     Rect.Top := 0;
     Rect.Left := 0;
     Rect.Right := Width;
     Rect.Bottom := Height;  
   end;

end;

constructor TMyPageControl.Create(AOwner: TComponent);
begin
 inherited;
 FHideTabs := false;
end;

procedure TMyPageControl.SetHideTabs(const Value: boolean);
begin
 if FHideTabs = Value
   then exit;
 FHideTabs := Value;
 Invalidate;
end;

end.

for i:=0 to PageControl1.PageCount -1 do
   begin
   PageControl1.Pages[i].TabVisible := false;
   end;