I run the business full time and my partner had no involvement this year. Can I list myself at 99% and my partner at 1%?

I don't think I can do 100% and 0%

Self-employed

If the business is a partnership, then the partnership agreement would dictate percentage ownership, regardless of involvement.

 

If this was solely your business, then it would make sense to NOT have your partner listed with any percentage of ownership. It is possible for your partner to be involved with the business, but they may merely be an employee or contractor.