A tundish assembly, including an element, for preventing or limiting steel reoxidization in the continuous casting of molten steel, is used in combination with a refractory nozzle. The element has an orifice engaging the outer surface of the nozzle, a main surface surrounding the main orifice and having a lowest level lower than the top outer edge of the nozzle inlet portion, and a periphery having an upper face surrounding the main surface of the element. The upper face of the periphery of the element is higher than the main surface of the element and is higher than the surface of the bottom well of the tundish. The main surface of the element is arranged so as to contact molten steel in a tundish.