Who is Ash Ketchum's girlfriend?

Ash has never decided to have a girlfriend, mainly because he is eternally ten. However, it was suggested that he and Misty, the Cerulean city Gym Leader from the first and second seasons, had a bit of a relationship. It is undetermined wether May,daughter of a Jhoto gym leader and a coordinator, has ever held affection for him; if she has, then Ash has not returned it. Dawn, the coordinator for the last three seasons; Diamond and Pearl, Diamond and Pearl Battle Dimension, and Diamond and Pearl Galactic Battles, is the same age as him and a character named Lyra attempts to pair the two up but neither of them are old enough to truly like each other.