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The past tense, and past participle of "split" is "split". I don't think that "splitted" is grammatical, though I dare say it gets used. Split infinitives involve the to-infinitive specifically.
Understanding the Context
The "to" not a "preposition"; it is a infinitive marker. Lastly, I found your arguments about "wanna" & "gonna" unconvincing and irrelevant because these words are informal and the argument about split infinitives is most certainly about prescriptivism. Does the "in" imply multiplication, in which case split in half is correct, or is it division? It sounds like the latter to me, but I've heard it used both ways.
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"Split in half" vs. "split in two" — which one is correct? What is the meaning of the following sentence? You have successfully split a hair that did not need to be split. Source: this post on the Programmers Stack Exchange.
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idioms - What does "You have successfully split a hair that did not ... What should be used in below sentence: “split” or “split up”, and why? We need to split up the background image of the website into two parts. When to use split and split up - English Language & Usage Stack Exchange