If I purchased a portion of my home in one year and then bought my partner's share in another year, how is depreciation calculated?

I originally purchased a 50% share of a property in 2009 (aggregate purchase of price of $175k for the property) and subsequently purchased my partner's 50% share (at a cost of $121k for her portion only) in 2016. I then paid off the mortgage in 2017 and began renting out the property in March of 2018. How do I calculate the Original Purchase Price, Available Date and Purchase Date in order to determine the depreciation (i.e. what amounts and dates should I use for each field)?

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The purchase price was whatever you actually paid in 2009 plus the amount you paid in 2016. Your final purchase date could be the 2018 and the date available is whenever you made it available for rent in 2018, usually the date you started advertising it or the date a renter could have moved in.