Using my time period of interest the three kingdoms of China (190-280), hopefully someone can provide a wider answer

Adoptions happened a fair few times, usually becuase a line died out or a figure was lacking a son, sometimes for political reasons or to take care of someone, usually it was between family members so a kinsman or related by marriage if needs be would be adopted.

The major warlord Yuan Shao was adopted across the powerful and wealthy Yuan line (he also tried to deny his eldest son Yuan Tan the heirship by adopting him back across Yuan lines so no longer his son). Wu general Zhu Zhi adopted his nephew Shi Ran (who later asked to be changed back to Shi clan), Sun He was adopted to the Yu clan as they had no males left and then later brought back into the Sun fold.

The warlord Cao Cao, whose father Song was adopted into Cao clan by the eunuch Teng, swapped grandchildren about so the lines of his dead sons like Cao Ang (killed in combat due to Cao Cao's folly) and Cao Chong (a great talent who died young) would continue. As one of Cao Cao's grandsons and the second Wei Emperor Cao Rui/Emperor Ming lacked children, he adopted Cao Fang from somewhere within the Cao lineage. The general Cao Zhen was adopted by Cao Cao, raised with Cao Cao's own children, after his father Qin Shao gave his life to protect Cao Cao while Zhen's son Shuang would hold regency for Cao Fang as an imperial relative.

Adopted figures were not shunned. Yuan Shao became head of his clan, as adopted to the more senior line, and leader of the warlords against court controller Dong Zhuo, his transfer was from someone living (Yuan Feng) with at least two other sons so his adopted (and dead) father Yuan Chang would have someone to ancestor worship him. Cao Cao did likewise to ensure his sons lines and sacrifices continued, it wasn't a case of they couldn't sacrifice to their ancestors but they were carrying out their filial duties to their adopted parents.

However if there were natural born sons later, the natural born son and lineage took priority. Shu's first Prime Minister Zhuge Liang struggled to have children so adopted Zhuge Qiao from his brother Zhuge Jin who was a senior adviser in Wu but when Jin's line was wiped out, since Liang had children since Shu sent back Qiao's son Pan to Wu and Liang's natural son had all the ranks bestowed upon up. Liu Bei, the founder of Shu-Han adopted Kou Feng as he lacked a son for a time and the Kou were related by marriage, Feng grew up and became a skilled general then was killed to ensure smooth succession for Liu Bei's later born natural son Liu Shan.

Sources: Rafe De Crespigny's A Biographical Dictionary of Later Han to the Three Kingdoms 23–220 AD (2007)

Various SGZ including the Zhuge clan by Chen Shou translated by Yang Zhengyuan