By agreement between you and your former spouse, you have a right to enter into a parenting arrangement with biological kids and/or step-kids.
If you and your former spouse cannot agree, you may make an application to Court to ask for time with your step-kids. If you are unmarried and the kids reside in Alberta, you may apply to Court under the provisions of the Family Law Act called “contact time”. This is designed for anyone who believes that they have a right to spend time with kids who is not a legal guardian of the kids. In fact, this is the same provision that grandparents, extended family, etc. would apply under to spend time with kids. If you are married, the Court would deal with your application simply under the Divorce Act which does not have a specific heading for your application as Alberta does, but they can deal with it by the general provisions of the Act by considering you to be “standing in the place of a parent”.
One consideration you will want to keep in mind is that in most cases the other biological parent will likely have priority in terms of time with the kids – if you are step-dad, biological dad will likely have priority and if you are step-mom, biological mom will likely have priority.
Of course, along with spending time with the step-kids comes child support. As the song goes “You Can’t Have One Without the Other”.