Trajan's successor was Hadrian

Hadrian married Vibia Sabina, Trajan's eighteen-year-old grandniece, at the time of his quaestorship, in 101. Given that the marriage would result in a scandalously bad relationship, Trajan himself appears to have had mixed feelings about it. It's possible that Plotina, the empress of Trajan, orchestrated the union. The view that the Roman Empire was a commonwealth with an underlying Hellenic culture was one that this highly educated, a powerful woman shared with Hadrian. Plotina and her extended family might continue to hold influential political positions and maintain their social standing if Hadrian were chosen as Trajan's successor. The assistance of Hadrian's mother-in-law, Salonia Matidia, a descendant of Trajan's adored sister Ulpia Marciana, was also available.

A civil war might break out if no heir is named, ushering in a chaotic, catastrophic wresting of power by a series of contending claims. An early nomination might be interpreted as a resignation, which would decrease the likelihood of a smooth transfer of power. Trajan could have legally adopted Hadrian as his heir by simply expressing his wish on his deathbed in front of witnesses while being cared for by his wife Plotina and closely watched. However, when an adoption document was eventually presented, it was signed by Plotina rather than Trajan and was dated the day after Trajan's passing. From that, Trajan's successor was Hadrian.