ANZ is one of the major banks in Australia.
I can't seem to find on their website or via Google which notes their ATMs dispense.
In particular, if I have a balance below $20 will I still be able to withdraw $10?
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I just visited my nearest ANZ ATM in Sydney and tried to withdraw $10 whereupon the machine informed me that it only dispensed $20 and $50 notes.
The machine clearly stated it was only talking about itself - so there is still a possibility that some ANZ ATMs dispense other denominations.
(Fortunately I was pessimistic and transferred a few cents between accounts in case $20 was the minimum I could get.)
I've never come across an ATM in Australia dispensing anything other than $20 and $50 notes. (I'm 28 and have lived here my whole life, have been with two of the major banks, and have also used other bank and non-bank ATMs from time to time).
That doesn't mean there aren't any - particularly it might be possible in some non-bank, i.e. private, ATMs (but then you'd also be paying a fee to use these, so it would not make much sense to withdraw only $10).
If you want to withdraw less than $20, you'd probably have to do it at a supermarket - most of them will let you take cash out, at Woolies or Coles I don't think it even requires a purchase. Some other shops may have cash out facilities as well, but may require a purchase. Generally there's no limit of the type of denomination you cash out, but there might be upper and lower limits depending on the store (eg. min $5 or $10, max $100 or $200, sometimes the max is a daily per-person limit).
As for why ATMs only dispense $20s and $50s, it's likely because using these two denominations they can dispense almost any amount you want (apart from $10 and $30), and no extra machinery is needed to handle the additional denominations (I don't know anything about ATM internals but it would probably add size and complexity to add more denominations). It's a generally accepted norm.
EDIT: Anecdotally, some ATMs particularly in high socio-economic areas may be dispensing $100, although I personally haven't come across any of these myself. I wouldn't be surprised if ATM's stop dispensing $20's one day and move to $50's and $100's!
Most ATM's in Australia only dispense $20 and $50 notes. However, I have noticed the ANZ 'Smart ATM' at my local branch, which was replaced in November, has an ad attached to it informing the user that it now dispenses the whole range of notes. I am in Perth but it seems to be the case in Sydney as well. As @Tim Malone has suggested, it would be a lot easier to use the 'Cash Out' function at a supermarket.