When a God takes avatar, what happens to the original God form. Does He remain as it is or is depleted or altered?
He remains the same, only manifests in a physical form:
"The avatar role-plays with deliberate and voluntary self-limitation. The avatar has infinite knowledge which he can choose to access, though ordinarily he does not, or else does so selectively"
In this also, there are two types of manifestation:
“For the purpose of creation, the Divine Being assumes several presiding personalities; each oversees the manifestation of particular truths. A given personality may choose to manifest as a full incarnation – in which case it is called an avatar – or as an embodiment of its particular truth – in which case it is called a vibhuti. Thus, avatar is God in visible form, and vibhuti is the manifestation of one or more of his infinite qualities. In other words, an avatar is a vibhuti, but a vibhuti is not necessarily an avatar. For example, Krishna is an avatar as well as a vibhuti, but Arjuna is a vibhuti only. Ushana, the brave king, likewise is a vibhuti”
-Excerpt from the book 'Being Different' by Rajiv Malhotra.