技 is mainly used in compounds: 技术 (technique/technology), 科技 (science and technology), 技能 (skill), 技巧 (technique/trick), 杂技 (acrobatics). Contains 扌 (hand) - skills are handiwork.
The hand radical (left-side form of 手) is the heart of the meaning: a skill is something the hands have learned to do well. It groups 技 with 抠, 抚 and 拨 - the family of refined manual actions and applied craft.
Provides the sound, drifting from zhī to jì along a regular Old Chinese pattern. It heads a phonetic series with 枝, 肢 and 歧. The branching meaning is unrelated, though one can picture a skill as branching out from the hand.
