The 1955 capitalization "(concerning Himself)" was changed to "(concerning himself)" in Urantia Foundation's 7th printing (1981). Although pronouns referring to Deity are usually not capitalized (see, for example, "himself" later in this paragraph), the original style may be important because the capitalization, if not an error, may have been intended to clarify that the self referred to is God rather than the creature, in a sentence that might otherwise be unclear.
Original Paragraph:
P46:4, 3:1.12
The fluctuations of the Father's presence are not due to the changeableness
of God. The Father does not retire in seclusion because he has been slighted;
his affections are not alienated because of the creature's wrongdoing. Rather,
having been endowed with the power of choice (concerning
Himself), his children, in the exercise of that choice, directly determine
the degree and limitations of the Father's divine influence in their own hearts
and souls. The Father has freely bestowed himself upon us without limit and
without favor. He is no respecter of persons, planets, systems, or universes.
In the sectors of time he confers differential honor only on the Paradise
personalities of God the Sevenfold, the co-ordinate creators of the finite
universes.