On the information page of your return, there are six categories of 'marital status' :
1. Married 2. Living common-law 3. Widowed 4. Divorced 5. Separated 6. Single.
The second of these, living common-law would apply to you if you are single, separated or divorced, and living with a common-law partner. You are considered common-law for tax purposes once you have had a child together, or have lived together for more than one year (whichever happens first).
Ontario Family Law creates certain rights and obligations after three years; but for tax purposes, one year is the rule.
As common-law partners, neither of you can claim an 'eligible dependent' deduction for a child, and you may not both claim GST/HST/Trillium benefits.