You must be doing something right if you’re able to buy this partner out. That’s good you’re in that position.
Now, save yourself some future agitation by deliberately determining what you need in a partner. Take the following steps:
1. Determine what the business needs to succeed (money, marketing/sales, operations/services, etc.)
2. Honestly consider what you do best and what you like to do (not necessarily the same thing)
3. Honestly consider your shortcomings and those things you detest (again, not necessarily the same thing)
4. Use that shortcomings/detest list as your starting point for identifying criteria for a partner
Another route would be to step back even further and ask yourself if you truly need a partner right now. Can you work solo for 6-18 months and get your own traction with some clients? That experience will likely further underscore what duties might be better handled by someone else.