When you own a co-op you own shares of stock in a corporation but it is treated for tax purpuses just as owning real property. Hence the answer is that you own, not rent.
If you are using the co-op as an investemnt and renting it out to a tenant, you have to report that income to the IRS.
When you own a co-op and are using it as your primary residence, a portion of the maintenance is usually tax deductable on your income taxes. This would be the portion of the maintenance that covers the co-ops underlining mortgage and real estate tax. This amount varies from co-op to co-op, speak to your accountant. Also, if you have a mortgage on the co-op, the interest you pay on that mortgagae is tax deductable.
If I can be of further assistance, please contact me.
Madison Estates & Properties, Inc.
Office: (718) 645-1665