I think I agree that, as far as routine expenses are concerned (taxes, mortgage, repairs), @Sarah515 can probably deduct 100% of those costs if they pay 100% of those costs. (Although I am willing to be persuaded otherwise.) However, deprecation of the main asset (plus depreciation of any improvements) must be split among the owners.
Also note that when you sell, you must recapture (pay tax on) any depreciation you did or could have taken as a tax deduction. So even if the father never deducts depreciation, that depreciation still occurs and must be repaid.
If the father doesn't want to be an owner, he can give you his half of the property and then you really will be a 100% owner. But a gift must be no strings attached, with no secret backdoor deal to repay him some day.
Or, the father could sell his interest to the daughter, who would consider it a second mortgage. The child would be the 100% owner and would deduct all expenses including depreciation, loan payments to the father would be a deductible expense against rental income, and the father would report interest income as taxable income (the father must charge at least the applicable federal minimum rate, or higher). However, note that taking out a second mortgage (even if financed by the father) could cause problems with the first mortgage.
If you can sit down with a good accountant and tell them what you really want (was dad helping you buy a property or does Dad consider this an investment that will earn him money as well), the accountant can figure out the best way to structure the arrangement.
