" Can I depreciate this property for the lenght my nephew lived there? "----> Of course.You recover the cost of income producing property through yearly tax deductions. You do this by depreciating the property; that is, by deducting some of the cost each year on your tax return.
You can depreciate your apartment building over 27.5 years on a straight-line basis. Assume that you purchased the apartment on march 3rd of 2005 for $186,000, then in the first year your annula accumulated depreciation expenses is $186,000/27.5*10/12=$5,636.Your annual accumulated depreciaiton expanse is $186,000/27.5=$6,764 in the second year.