Hristos Voskrese!
Father Serge is indeed correct, there is a Church under the Moscow Metropolitan, and it would be fair to call them a
'split' though I am not sure how they would take to that term themselves. They don't have issue with our formal Heirarchy (or validity of such) or the belief system in place - it is literally 'a people issue' they have - with parishoners and clergy specifically; a sad state of affairs indeed . They are located some 2 or 3 kms from the proper Sydney parish under the Belaya Krinitsa concorde. Having said that, when a resident priest is not at their 'home church', many return to the BK one. Only the 'die-hards' remain at the smaller one. It is upsetting as many families may be split between the two. I look to my Grandmother - her sister goes to that Church, as do most of her children and grandchildren - whilst my Grandmother and her other sister (and of all us off-spring) went/go only to the other. I have been to the other one twice - once for a funeral and once to welcome a visiting bishop.
I digress.
The
third Church issue interests me. I have a theory on this. There are some Old Calendar Greek Churches in Sydney which are sometimes wrongly identified as Old Ritualists (well not
wrongly, but when we take Old Ritualist to mean
Russian Old-Rite it causes confusion). However - I dont believe this is the 'third church' of which we have heard reference to. I believe it may be the Old Believers proper - and by that I mean the bezpopovsty. Yes, most bezpopovtsy ended up (logically enough) as part of the BK Church, though there are still those that refuse the priesthood (though who they are and where to find them I would have no idea). The only issue is that they would certainly not have any Churches of their own when it comes to physical buildings, nor would they be a 'congregation' as such in one cluster, but rather just more scattered families I would imagine. Still, reference to a 'Church' does not always mean a building with a dome on the top of it, does it now?
Perhaps the BK Church in Melbourne was seen as the third church? Perhaps even one of the ROCOR may have ben mistaken for an Old Rite Church? The ROCOR tend to be somewhat more conversative at some parishes???...

My last suggestion would be (and I think the most plausible), that as a result of the split in the ROCOR over the unification with MP, perhaps the separated ROCOR churches which have popped up throughout NSW may have been mistaken as Old Rite - as they are seen as Russian Orthodox - but of a 'different' jurisdiction and are in sense, "
Raskolniki" (just like the Old Rite) for not accepting church changes?... It may be a possibility?.... There is a lot of tension between these two groups, and I believe one such church was set up directly across the road from the other - which could result in them being seen as 'schismatics'?? I wont comment on that any more as I know nothing about their separation and don't want to offend anyone with erroneous comments...
I can't think of any other reasons to be honest with you. If anyone hears any more on this - I admit myself curious...