Patricia Joanne Pullman was a con artist, who was wanted by the authorities for her murdering her father. (PROSE: The Gallifrey Chronicles) Pullman eventually adopted the name "Trix MacMillan".
She first met the Eighth Doctor when she had been hired by Sabbath to pose as a descendant of Tsar Nicholas II. After Sabbath had punched a hole in reality and the Doctor had to give chase, Trix asked if she could come along. The Doctor refused to let a con artist and a thief aboard the TARDIS, but she stowed away nevertheless, avoiding detection by the Doctor and his companions for a long time. (PROSE: Time Zero)
A shadowy figure later appeared and implied to Lyeene that Trix had stowed away on the TARDIS and avoided detection. (PROSE: The Last Resort)
When Trix was discovered, the Doctor did not punish her or make her leave the TARDIS, to Anji's annoyance. Like many of the Doctor's other companions, Trix had a habit of wandering off, and had small adventures of her own before ending up back with the Doctor. (PROSE: Timeless)
However, she and Fitz would continue to travel with the Doctor for a time. On one trip, they discovered a planet where temporally-anomanous Neanderthals were being herded as temporal weapons in preparation for a time war. (PROSE:We Can't Stop What's Coming)
Trix often disagreed with the Doctor. However, over time the Doctor helped her come to terms with herself and feel settled in her life. (PROSE: The Gallifrey Chronicles)