That is indeed what happens, the molten iron is taken straight from the blast furnace, and then is reacted with oxygen to burn out all the carbon and other impurities, carbon is then added to the required amount, along with many other additives such as manganese,molybdenum, chromium etc to produce the required type of steel. There is an excellent description in the early chapters of "Hardening,Tempering and Heat Treatment" by Tubal Cain (Thomas D Walshaw, ISBN 978-085242-837-5 SI model Books) What I have just told you however is a very simple description of a very complex process! Metallurgy is not for the faint hearted!