Chobits(2000)

After moving from the countryside into the big city, poor college student Hideki Motosuwa finds himself down on his luck. All he wants is a good job, a girlfriend, and his very own “persocom” - the latest and greatest in humanoid computer technology. Hideki’s luck changes one night when he finds Chi - an adorable, but seemingly broken, persocom thrown out in a pile of trash. After taking her home, Hideki discovers that Chi is more responsibility than he expected - and that there’s much more to his cute new persocom than meets the eye.

(Source: Kodansha USA)