Actually, one user had it down pretty well. The contrails are formed by the extreme heat in the aircraft engines reacting with extremely cold air found at high altitudes. The thickness of the contrail itself, usually whether or not it stays place in the air for long or dissipates, depends on the moisture located in the air at the time. However, they are usually formed regardless, unless it is unusually dry air, because of the speed to which the temperature of the air is changed...most undoubtedly in microseconds. Any change in temp that has that vast of a range will produce thick moisture. Then, if the air is cold enough, the newly created moisture becomes tiny ice crystals, suspended in the upper layers of the atmosphere. These are the ones that never seem to go away and are usually very thick.
Hope this helps.