For business use of home, you cannot include shared spaces. You can only use places used exclusively for the use of business, with some exceptions for individuals who operate in-home daycare centers. You can find more about that HERE.
With all tax deductions, including the actual expense home office deduction, only items that you personally pay (and are obligated to pay) are deductible by you.
If you are using the actual expense method for your home office expenses you can enter the square footage of your exclusive office space into TurboTax along with the full square footage of the home. You then enter the expenses broken down by category for you in the software. The software will do the math for you - but yes, it is much as you describe- the percentage of the bills attributed to the percentage of space that is office are used to create the deductible amount.
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