I tend to leave all the accounts on the trial balance even if they are zero balance accounts. just because they are zero balance accounts does not mean that dont have any activity. For instance we have a clearing account for our payroll. The balance is zero-ed out pretty quickly, but if i were to pass my trial balance on to an auditor it would make them aware i have multiple cash accounts rather then just one operating account. Same with your AP account, say this account has a zero balance as a result of an improper entry that was previously booked and it actually should have a balance. It doesnt hurt anyone or anything to have a few zero balance accounts on the trial balance. Un-used or inactivate accounts can be deleted if they dont have a balance.