Australia to South Africa to Morocco. All travels are 4-5 days apart. So which ticket do I book with which passport? Which passport do I use to enter and exit to the next country?
This answer assumes that each of the countries allows you to be a citizen of the other two countries, and that your name is the same in all three passports.
It doesn't usually matter what passport you give the airline when you book the ticket. You can generally check in for different flights on the same ticket using different passports.
Each time you check in, show the passport of the country where you will arrive at the end of that trip, even if that's not the passport you used to enter the country you're leaving. If you are using another passport for visa-free transit, or if you used another passport to enter the country you're leaving, show the relevant passport to the airline if they ask about it. If the agent looks concerned, you can offer to show the passport without waiting for a question.
For each country you visit, pick one passport and stick with it. Always show that passport to officials of that country. For countries of which you are a citizen, use the passport of that country.
In truth, it's really not that different from I have two passports/nationalities. How do I use them when I travel?; it's only slightly complicated by the fact that there are three countries rather than two.
Typically, you don’t need a passport when booking a ticket.
You will need a passport to check in, be it online or in the airport. At this time, simply always use the passport of the country you are flying to.
The airline is not concerned about your citizenship(s), they are concerned that you are allowed to enter the country at the destination. If you show a passport from that country, you are obviously good to go there, and that’s all they care about.
I have dual but not triple citizenship and I used to travel a lot for business so I had to do some research, but as I am not from any of the countries you have listed, you can take my advice only as a suggestion of facts you need to find for yourself.
The most important point is that you can not claim the protection of any other country in a country for which you claim to be a citizen. In other words, you can not use your South African passport in Australia and vice versa. In practice, this means you can not travel on two passports at the same time. You can carry other passports with you, but you can't change passport half way through a journey so I would strongly recommend that you keep the extras in sealed envelopes from before departure until after arrivals. If immigration are opening sealed envelopes, you have bigger problems to deal with then having extra passports.
Since it is easier to leave a country that you are a citizen of as a foreigner then it is to arrive as one, I would recommend you break you journey into legs so that you can travel on the passport of the country that you are going to. That said, countries requiring exit visas for their own citizens can be a problem but I don't think that should affect you. Talk to their counsel for each of the countries and ask their advice before you travel. There is another reason to talk to the counsels of the different countries rather then get the advice from strangers on the interwebs, and that is that some countries charge tax based on residency. If you arrive on one passport and leave on another, then their tax office might not know that you have left and decide that you owe them money.