Although the T Rex is the biggest dinosaur that is known to be the biggest dinosaur on earth the Giganotosaurus dinosaur is a bit larger than the T Rex.
So the Giganotosaurus would be the biggest dinosaur above the T Rex.
However there is another species of dinosaur that is larger than the T Rex and the Giganotosaurus which is the Spinosaurus.
So as far as we know as of now the Spinosaurus is the largest species of dinosaur that lived on earth.