This paper analyses the ways in which product fragmentation (producing part of a product in one country, and a part elsewhere) can be used by multinational firms which have different productivity to serve the market abroad when product chains can be internationally and arbitrarily fragmented. Product fragmentation is thus an additional option to serving markets abroad by either horizontal or vertical FDI. Upon opening a market to trade, firms with the lowest productivity will exit, those with intermediate productivity will export, and those with higher productivity will choose fragmentation. Among the latter, the more productive a firm is, the more product chains are allocated abroad. Firms with the highest productivity will choose horizontal FDI. At a sector level, the more prone to fragmentation a sector is, the lower will be the ratio of exports to FDI sales.