The Canada Pension Plan requires "cohabitation in a conjugal relationship" for certain benefits to be transferred on the death of a partner. Most of these criteria (as listed in Betts v. Shannon (2001) CCH CEB & PGR No. 8661, pp. 6775-6782) are useful indicators for a genuine case of "cohabitation" for immigration purposes also. Note also that:
Cohabitation in this context is not synonymous with co-residence. Two people can cohabit even though they do not live under the same roof and, conversely, they may not be cohabiting in the relevant sense even if they are living under the same roof. (Hodge v. MHRD, 24 SCC 65)
You might have to go to an appeal if you wanted to prove that you were cohabiting without living together, but it has been done before in an immigration context. (See Fantin v. Canada (Citizenship and Immigration), 2005 CanLII 56919 (I.R.B.)
Here is the list from Betts v. Shannon (everything is here, for completeness, despite the fact the the parts about deceased partners obviously don't apply to the immigration context):
Cohabitation in a conjugal relationship will usually involve many of the following elements or questions, although not necessarily all of them:
1. Financial interdependence e.g., shared bank accounts, credit cards with the same number, the acquisition and ownership of property.
2. A sexual relationship. Did the parties have sexual relations? If not, why not?
3. A common residence. Did the parties live under the same roof? Did they eat their meals together? What were their sleeping arrangements?
4. Expenses for each other on special occasions. Did the parties buy gifts for each other on special occasions?
5. A sharing of responsibilities in the running of the household. Who prepared the meals? Who washed the clothes? Who did the shopping? Who looked after the maintenance of the home?
6. A shared use of assets such as cars, boats, etc.
7. A shared responsibility in the raising of children.
8. Shared vacations.
9. The expectation each day that there will be continued mutual dependency.
10. Each party named a beneficiary in the will of the other.
11. Each party named a beneficiary in the insurance policy of the other.
12. Where each of them kept their clothing.
13. In cases of illness, who cared for the one who was ill? Which one visited the ill one if in hospital?
14. Who had knowledge of the medical needs of the other?
15. Communication between the parties.
16. Public recognition of the parties.
17. The attitude and conduct of the community and the parties' families towards the parties, and, in the particular circumstances, the common-law relationship between the deceased and the respondent
18. What marital status was declared by the parties on various applications, on other forms, completed by them?
19. Who took care of the deceased's funeral arrangement? Was there a funeral notice, and, if so, how were the parties described therein? Who was billed for the funeral costs? Who paid for the funeral? Who attended the funeral? Where did they sit?
One more useful quotation from Cahoon v. Allred (September 9, 1997) CP 5556 (PAB):
Parties to a relationship who maintained their separate residences were not cohabiting, regardless of the number of times or nights they spent together. Where they did not share the use of the furnishings, had no common bank account and neither took responsibility for the other's basic living expenses, there was no common enterprise one expects when two people are cohabiting in a conjugal relationship.
Keep that in mind if you are claiming a conjugal relationship. Obviously, you will have separate residences in a "conjugal partnership" immigration context, but there is some importance attached to bank accounts and basic living expenses in most conjugal relationships (whether a "common law partnership" or "conjugal partnership" or even a marriage).
One last quotation:
The weight to be accorded the various elements or factors to be considered in determining whether a couple is in a conjugal relationship will vary widely and will be almost infinitive. Brandon v. MHRD (November 30, 2001), CP 14937 (PAB)