No, no. It was by his choice. They didn't kick him off. Christopher Eccleston probably read the script for second season and decided he didn't want to get together with Rose! :p Actually, he said it was because he didn't want to get pigeon-holed into being the Doctor, like how Patrick Stewart will always be seen as Jean-Luc Picard. I can really see that happening if he did stay because I honestly like all the episodes with the 9th Doctor whereas I probably only like half of each season from the 10th.

(Wish I had source material to give the episodes to you.)