The quality or state of being egotistical; the degree to which someone demonstrates excessive self-importance and self-centeredness.
From egotistical (adjective form of egotism) plus -ness (a suffix that turns adjectives into nouns expressing a quality). This creates an abstract noun describing the trait itself.
Egotisticalness is a clunky but precise word—by adding -ness to egotistical, you can talk about self-centeredness as an abstract quality or degree, so you could say someone's egotisticalness was growing.
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