Zero production was never split. The Army and Navy had their own design and production channels, and rarely shared anything the intraservice rivalry was that strong.
The Type 1 Ki-43 "Oscar," the IJA's primary fighter during much of the war, bore a very strong resemblance to the Zero fighter and often caused quite a bit of confusion among Allied pilots.
Later in the war, as the IJN's carrier forces were whittled down and the Navy's role became progressively more marginalized by the simple fact that there were fewer and fewer places for them to place aircraft as the Allies island hopped across the pacific, many of the remaining Zeros were assigned to defend the home islands and to serve as Kamikazis.
The Army was primarily in charge of home island defense, so it would have been in charge of whatever Zeros were left, but they were always flown by Naval aviators, not Army aviators.
"The gift which I am sending you is called a dog, and is in fact the most precious and valuable possession of mankind" -Theodorus Gaza
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