Complex sentence: Bugs immediately claims Mars as his own (using a metal carrot with a flag inside), in the name of Earth; however Marvin does not agree with this and decides he will not allow Bugs to take his planet away from him.
Split into simpler sentences: Bugs immediately claims Mars as his own (using a metal carrot with a flag inside), in the name of Earth. However Marvin does not agree with this and decides he will not allow Bugs to take his planet away from him.