[1] The family migrated to Adelaide, South Australia in 1837; Randolph and his brothers Jefferson and Augustine were educated at home by their father and at a school run by D.

Randolph Stow showed great ability as a boy[2] and was articled (apprenticed by contract) to a firm of lawyers, Messrs. Bartley and Bakewell.

By 1875 Stow was the unchallenged leader of the bar at Adelaide, and on 15 March 1875 was appointed judge of the Supreme Court,[2] in place of William Alfred Wearing, who died on the wreck of the SS Gothenburg.

[2] At the time of his death there was a general feeling that South Australia had lost a great judge, and many years later Sir John Downer who became a Q.C.

A commanding presence, a striking face, an exquisite voice, unusual swiftness in comprehension, with an immense combination of eloquence and power".