A business partner and I are starting up a store which will have an online presence as well as a physical retail space. How do I divide the profits if we are unsure which side will be more profitable?

Normally in your partnership agreement you will outline what each individual is contributing to the business and how profits will be divided. I strongly encourage you to seek an attorney and have a formal partnership agreement so that you clearly outline what is expected and given to each partner.

The way to divide profits is essentially however you two deem you want them divided. Normally it would be based on the percentage of ownership each has in the business.