Abstract: The present invention is an apparatus and method for continuously separating, removing and purifying the solid residue, resulting from the conversion of hydrocarbons into carbon and hydrogen, from the homogeneous phase of different density contained in a cracking reactor with which said solid residue is not soluble, and where the separation of the solid carbon occur at two subsequent moments: a first separation occurs inside the reactor between the reaction products, including carbon, and the melting bath; a second separation then occurs outside the reactor between the carbon and the gas produced in a separation system (1) of the solid phase from the gas phase, where said separation system (1) also includes carbon purification.