As Yifuj pointed out... you always want shares in your name -...

As Yifuj pointed out... you always want shares in your name - whether that be through CHESS or Issuer sponsored.

Paddywaggon, I am not sure who told you holding shares through a custodian is the safest. As has been pointed out this just adds an extra layer between you and your shares. In such a scenario, although you are the beneficial owner, you are not the legal owner. This can cause all sorts of issues when things go bad. Unfortunately, there are countless stories of custodians doing the wrong thing.

Its usually pretty easy to differentiate in Australia which brokers use a custodian style, because the brokerage is invariably cheaper. IG markets is a prime example. Pretty much the cheapest brokerage around, but the share are never legally held in your name. 

In most other countries, like the US, custodian held shares are just the norm. But in Australia. it is definitely advantageous, I think, to hold full title to your shares. Especially given the ease in which it can be done with a variety of brokers.