Correct. It all depends on the structure of the HOA. Newer ones are "fee simple" where anything attached to your unit are your responsibility. This shifts the financial burden onto the unit owner. There's also homeowner associations vs condo associations. Each have their own rules and headaches.
The "study" you are referring to is a Reserve Study which covers all items under the association's responsibility. It will determine how much $$ the association needs to have in reserve in order to replace everything at once.
My old 179 unit condo association's projected reserve is in excess of $1M primarily because of the roofs but that is what these studies will give you. A proper study can cost $25K or more. This is not something an accountant would prepare. It is done by an engineering firm. Here's one company in Central NJ: