Adric

Adric was a companion to the Doctor in his fourth and fifth incarnations.

Early life on Alzarius
Adric was an Alzarian born on the planet Alzarius in the parallel universe of E-Space in the 32nd century. He was ranked as an elite and awarded a gold star badge for mathematical excellence because he could do large sums in his head. His brother Varsh belonged to a gang of teenage thieves; Adric wanted to join them but was refused. Varsh asked him the embarkation question "Where will you be when the starliner leaves Alzarius?" to which he replied he would be somewhere else entirely. This would be true; he would be onboard the TARDIS when it took off. To prove himself to the gang he tried to steal river fruit but failed. (DW: Full Circle).

E-Space adventures
Adric hid aboard the TARDIS until discovered by the Fourth Doctor and Romana. He pretended to share the agenda of the Three Who Rule, a trio of vampires who lorded over a small community. He tried to save Romana from being sacrificed but failed; both were saved by the Doctor. (DW: State of Decay)

After Romana
After Romana left, (DW: Warriors' Gate) Adric and the Fourth Doctor travelled together. The Doctor genuinely came to like Adric. (PDA: Divided Loyalties) Soon after leaving N-Space, they went to Traken and met Nyssa. After apparently dispatching the threat of the Master, and returning the Keepership to is rightful heir, (DW: The Keeper of Traken) the duo travelled widely. The Doctor constructed another version of K9, who joined them on their journeys. (DWA: Inter-Galactic Cat, Conundrum, Planet of Paradise, Plague World, Just a Small Problem)

At some point prior to the Fourth Doctor's attempt to fix the TARDIS' chameleon circuit, (DW: Logopolis), the Doctor dispensed with this newer K9.

With the Fifth Doctor
Adric's relationship with the Doctor deteriorated after the Fourth Doctor regenerated and Tegan and Nyssa began travelling in the TARDIS. (DW: Logopolis, Castrovalva) Adric believed that the girls were a hindrance to his relationship with the Doctor. He also had a clear preference for the Fourth Doctor, whom he regarded as the "real Doctor", and whom he missed after spending time with the Fifth Doctor. (PDA: Divided Loyalties)

Often frustrated by his clumsiness and fiercely competitive, Adric struggled to find a useful role in the TARDIS crew.

He eventually told the Doctor that he wanted to return to E-Space. After showing the Doctor his computations to engineer the return, Adric confessed that he really wished to remain on the TARDIS. He became caught up in an attempted Cyberman invasion, which led him to sacrifice his life by remaining on board a crashing spaceship. The ship, Captain Briggs' freighter, was traveling through time. With Adric onboard, it crashed into prehistoric Earth, causing the extinction of the dinosaurs. (DW: Earthshock)

Adric's death haunted the Doctor for many years, His tenth incarnation watched Adric die again -- this time as a manifestation of the TARDIS Matrix. (IDW: The Forgotten)

In an alternate version of these events, after interference by the Doctor during an attempt to recover his TARDIS, his sub-consciousness helped Adric break the final logic code on the Cybermen's computer. This let Adric land - and survive - on Earth. Adric created a City of Excellence and ruled over a sentient race of scorpions that evolved in place of the dinosaurs. Adric created this world with Block Transfer Computations. Five hundred years later, Adric met the the Doctor and Nyssa, and accompanied them back to the Victorian era. Adric finally died after helping the Doctor recover his TARDIS from Thomas Brewster. (BFA: The Boy That Time Forgot)

Personality
Adric was a mathematical genius. He was proud of his Elite status, claiming that it made him better than others. Adric wanted to join his brother Varsh's gang, the Outlers, and tried to steal fruit to prove himself. He said he was tired of how he was pushed around on the Starliner. When his brother died, he kept his belt, a symbol of Outler membership. (DW: Full Circle) He pretended to go along with the plans of the vampires in a ploy to rescue Romana, with whom he got on well. (DW: State of Decay) Aukon sensed that Adric had the strength of spirit to survive becoming a vampire. (EDA: The Eight Doctors) He ultimately gave up his life by remaining on board Captain Briggs's freighter to prevent it from crashing into the Earth. He died holding his brother's belt. (DW: Earthshock)

Though Adric could be boastful and rude, he was fiercely loyal to the Doctor, and enjoyed a good relationship with the Time Lord (especially during the Doctor's fourth incarnation, which Adric preferred) who acted as his mentor. Adric showed bravery many times; for instance when defying the Master (DW: The Keeper of Traken) and when he gave his life to save the Earth. He also had a good sense of humour. (DW: Earthshock)

Other information

 * The last word of the Fifth Doctor was "Adric?" (DW: The Caves of Androzani)