Hi Rafael,
Your spouse does not have an automatic right to your assets. What you solely own is yours alone, and vice versa for your CL spouse. So, no, you do not owe her half the interest of your car, nor half the value of your RRSP.
Any assets jointly held would be divided. So, if the RESP is in both your names, each of you are entitled to half, but in most cases both parties claim to have $0.00 interest since the RESP is for the child(ren).
Unfortunately, you do not have an interest in the home. If it's in your CL spouse's name only, she can do what she wants with the house, including denying you entry, without your consent.
You aren't responsible for her debts nor is she responsible for yours. You will have to pay half of all joint debts.
I believe Alberta allows common law spouses to claim unjust enrichment, but I'm not sure. When making an unjust enrichment claim, a party argues that although they don't have an automatic right in an asset solely owned by another party, they should as a result of their financial or other kind of contribution to that asset. So, with the home, you could argue that although you aren't in title, you contributed financially and through other means (housework, yardwork, etc.) thus earning an interest in the home. Please keep in mind that your spouse could also make the same kind of claim against your RRSP.
I suggest you speak with a lawyer to clear the air on whether Alberta allows this kind of claim.
Lindsay
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