This book is mine as much as anything!
What does this mean?
Does this mean, "This is REALLY MINE!!"
I would want native speakers' opinion.
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The idiom here can be correctly identified as 'as much as anything', as you state.
It would only make sense in certain contexts:
_"Only the paintings and the silverware are yours."
_"This book is mine as much as anything!"
The phrase "as much as" is used incorrectly in the example you listed.
"As much as" is an idiom meaning "to the same degree as"
So saying "this book is mine as much as anything" is like saying "this book is mine, to the same degree that anything is mine", which isn't saying much.
A more appropriate use of the phrase would be to say "this book is mine as much as your book is yours."
as much as anything, as much as anything else: no less than other things
You need to look at reliability and safety as much as anything when buying a car.
It was war, as much as anything else, that made an artist out of Westermann.
Answer copied from Free Dictionary.