Did the two sheikhs, Ibn Baz and Ibn Uthaymeen, issue fatwas prohibiting masturbation absolutely, or did they permit it out of necessity, and what is this necessity?

The Fatwa (definition)'s Summary:

Masturbation out of necessity is a matter upon which scholars have differed. As for Ibn Baz, he absolutely prohibits it, arguing that it is a reprehensible and harmful habit, contrary to Islamic law. He cites the noble verses that describe believers as those who guard their private parts, except from their wives or those whom their right hands possess. As for Ibn Uthaymeen, he generally prohibits it, but permits it when there is a necessity, whether it be a religious necessity (such as the fear of falling into zina [unlawful sexual intercourse]) or a physical necessity (such as the fear of physical harm if excess [sexual fluid] is not expelled).