What you have to understand first of all is that if you have a common law marriage, then you are married for all purposes everywhere forever, even if you move to another state without common law marriage, unless you go to court and get a real divorce with real lawyers. This includes filing married tax returns. If you file married for one year, you have to file married for every year until you get a legal divorce. You can't go back-and-forth between married and single depending on what has the best tax advantage.
If you are married, either with a formal marriage or a common law marriage, then either you or your spouse can claim your children or step children as dependents, as long as they meet the other tests of support and residency.
However, you must also file using a married status. Both of you have to file as married filing separately or married filing jointly. You can't file single, and if you've been living together, you can't file as head of household. Filing separately generally has higher taxes, as many deductions and credits are limited or disallowed.
You should think about filing one joint return with your spouse.
If you decide to file married filing separately, then you and your spouse have equal rights to claim biological and step children as dependents. You can divide the dependents anyway you want. Just don't claim the same dependent twice.
