how to remove distribution db from publisher?

Check the sp_dropdistributor @no_checks = 1

Before executing please check the details of this sp here:
http://technet.microsoft.com/en-us/library/ms173516.aspx 

I ran that earlier using that ms provided doc and got the following errors:
Msg 14166, Level 11, State 1, Procedure sp_replicationdboption, Line 203
Disable publishing ignored error msg 3906, severity 16, state 2: Failed to update database "Advantage" because the database is read-only..
Msg 3930, Level 16, State 1, Procedure sp_replicationdboption, Line 240
The current transaction cannot be committed and cannot support operations that write to the log file. Roll back the transaction.
Msg 266, Level 16, State 2, Procedure sp_replicationdboption, Line 0
Transaction count after EXECUTE indicates a mismatching number of BEGIN and COMMIT statements. Previous count = 0, current count = 1.
Msg 266, Level 16, State 2, Procedure sp_dropdistributor, Line 0
Transaction count after EXECUTE indicates a mismatching number of BEGIN and COMMIT statements. Previous count = 0, current count = 1.
Msg 3998, Level 16, State 1, Line 1
Uncommittable transaction is detected at the end of the batch. The transaction is rolled back.

why is database " Advantage " in read only mode. ?

it looks like you need to change it for readonly to readwrite in order to update system tables.

When you create the distributor make sure you give a network location for the snapshots where they will be created when needed.

That's the kicker... The Advantage db is in read/write mode. The server, where distribution lives that's our log shipped server. On that server we've log shipped Advantage db which is standy mode. I didn't get it why it's grabbing that db?

>> I didn't get it why it's grabbing that db?

because every action on the database is log shipped to the other server .

Please close this. Thank you.

Thanks