TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Process: The mixture of free fatty acids is fractioned into the phases L and S by a fractional crystallization method, which consists in a controlled cooling down during, which the free fatty acids of the mixture with saturated or substantially saturated acyl-moieties crystallize and precipitate from the mixture forming the phase S, while the free fatty acids with unsaturated or substantially unsaturated acyl-moieties remain liquid forming the phase L, where both phases are then separated by simple filtration or decantation or centrifugation. The phase L is esterified with a 1-5C monofunctional alcohol in order to produce alkyl fatty esters as bio-diesel. The fatty acid soaps are obtained by neutralization of free fatty acids to obtain hydrolysis of the fats and oils. The phase S is: transformed into linear or substantially linear paraffins as bio-naphtha by hydrodeoxygenation or decarboxylation or decarbonylation of the free fatty acids; and transformed into linear or substantially linear paraffins as bio-naphtha by decarboxylation of the free fatty acids on basic oxides including alkaline oxides, alkaline earth oxides, lanthanide oxides, zinc oxide, spinels, perovskites, calcium silicates, either as bulk material or dispersed on neutral or basic carriers and on basic zeolites. The hydrodeoxygenation or decarboxylation or decarbonylation is conducted in the presence of hydrogen and of at least one catalyst including nickel, molybdenum, cobalt or mixtures of nickel-tungsten, nickel-molybdenum, cobalt-molybdenum, nickel-cobalt-tungsten, nickel-cobalt-molybdenum, nickel-molybdenum-tungsten and cobalt-molybdenum-tungsten oxides or sulfides as catalytic phase, preferably supported on high surface area carbon, alumina, silica, titania or zirconia or group 10 and group 11 metals or alloy mixtures supported on high surface area carbon, magnesia, zinc-oxide, spinels, perovskites, calcium silicates, alumina, silica and/or silica-alumina. The hydrodeoxygenation reaction is carried out at a temperature of 200-500 degrees C, under a pressure of 1-10 MPa (10-100 bars) and with a hydrogen to feedstock ratio of 100-2000 N1/1. The decarboxylation reaction is carried out at a temperature of 100-550 degrees C in absence or presence of hydrogen under a pressure of 0.01-10 MPa (1-100 bars). The decarboxylation of the soaps reaction is: carried out at 100-550 degrees C under pressure of 0.1-10 MPa and in presence of water; and carried out with water to feedstock ratio of at least 1 mole water per mole of soap. The feedstock is mixed with steam in a ratio of 0.2-1 kg steam per kg feedstock, preferably 0.3-0.5 kg steam per kg feedstock. The mixture is heated up to a temperature of 750-950 degrees C at a residence time of 0.05-0.5 seconds. The bio-naphtha is cracked, preferably steam-cracked to obtain an ethylene to methane in weight ratio of at least 3. Preferred Components: The complex mixture of natural occurring fats and oils include vegetable oils, animal fats, inedible highly saturated oils, waste food oils and/or by-products of the refining of vegetable oils. EXAMPLE - No suitable example given.