Change the Existing Topology of a MySQL Replication Setup
Based strictly on your question, the topology you want is not possible.  Why?

Here is what you presented (call it Topology#1)

    a -&gt; b
    b -&gt; c
    c -&gt; a


and you want it to be (call it Topology#2)

    a -&gt; c
    b -&gt; c


Since ServerC cannot execute CHANGE MASTER TO with multiple host/port combinations, Topology#2 is mechanically impossible.

I have addressed this as to why IT IS NOT POSSIBLE:


Feb 03, 2012 : One slave, multiple masters MySql
May 15, 2011 : Is Multi Master Single Slave possible in mySQL DB? (My ServerFault Post)


Now, it you want to turn Topology#1 into this (call it Topology#3)

    a -&gt; b
    a -&gt; c


this is quite possible. Here are the steps:

STEP01) On ServerB, run STOP SLAVE;

STEP02) On ServerC, run SHOW SLAVE STATUS\G and check to make sure Exec_Master_Log_Pos is no longer updating.

STEP03) On ServerB, run SHOW SLAVE STATUS\G.

STEP04) Record Relay_Master_Log_File (call it RMLF) and Exec_Master_Log_Pos (call it EMLP) from STEP03 (For the sake of example, let RLMF='mysql-bin.000345' and EMLP=98765)

STEP05) On ServerC, run the following (Using RMLF and EMLP from STEP04):

STOP SLAVE;
CHANGE MASTER TO
master_log_file='mysql-bin.000345',
master_log_pos=98765;`
START SLAVE;


STEP07) On ServerB, run START SLAVE;

STEP08) On ServerA, run STOP SLAVE;

Going forward, have all INSERTs, UPDATEs, and DELETEs occur on ServerA only.