As discussed under 1 Nephi 19:10, the Book of Mormon text uses the adverb up in the phrase “to yield oneself (up)” when surrendering to an opponent in war:
But the up is lacking when voluntarily yielding to someone else’s power:
Consistent with this distinction, the 1830 reading with up in 3 Nephi 4:16 is very likely the correct reading.
This conclusion is supported by errors in the early transmission of the Book of Mormon text. On the one hand, we find considerable evidence that Oliver Cowdery frequently omitted the up; see under Alma 27:3 for a list of five clear examples, three that were momentary and two that were permanent. On the other hand, there are no cases where the 1830 typesetter accidentally added an up (although in two cases he accidentally omitted it, in Alma 62:22 and in Ether 13:8). In other words, the odds are high here in 3 Nephi 4:16 that Oliver is the one responsible for the variation. The critical text will therefore maintain the up in the phrase “to yield themselves up”.
Summary: Maintain in 3 Nephi 4:16 the up in the verb phrase “to yield themselves up” (the 1830 reading); Oliver Cowdery was prone to omit the adverb up, but the 1830 typesetter never added it; usage elsewhere in the text shows that the up in the phrase “to yield oneself (up)” is expected when surrendering in war.