How to randomly display players on spawners at the start of the game?

Almost already everything has been said in the title but I would add that:

I tried to spawn the players in this way by creating a family gathering all the spawners.

I gave the instruction "PlayerX -> go to spawners (the familly)" but it doesn't work because all the players appear in the same place...

You can use 'system pick a random instance of spawner > set position to spawner'. To ensure they don't spawn on the same one again you can use a variable. 'Pick a random instance of spawner, where spawner.var=false > set position spawner, set spawner.var=true'

It's probably a bit silly but I don't know how to program 'Pick a random instance of spawner, where spawner.var = false> set position spawner, set spawner.var = true'.

For the moment I have just managed to have each player spawned on 1 spawn but it sometimes overlaps.

It's not really clear why you're using a family. Are all the spawners separate objects or are they instances of one object?

Each spawner is an object

Add a family instance variable, maybe a bool is good enough.

On the left conditions add pick a random instance of 'family', its under system.

Then add another condition with it, family compare variable family.var=false

Then on the right actions say : family spawn player, and also another action family set variable to true.

This is what I had tried to do just before but weirdly it does not work.

Let's see a screenshot of the events

Of course:

(there is a "on start of the layout" on the top)

This won't pick correctly, notice you are setting the position to a random instance and the variable is in a sub event. It should be pick random instance with the variable condition attached as the same condition not as a sub event. Then the 2 actions appear on the right of this. It should look like one block event for each player.

If there are enough spawners in the level with variable set to 0 then it should work. If a player doesn't spawn then it likely cannot find a spawner. If it's still not working please post a screenshot of the new event structure after making sure enough spawners are in the layout.

Now verify that the 3 of them have the variable set to 0, and that the 3 player objects are also in the level? Also that the 3 of them are in the family (kind of confirmed by checking the variable anyway)

The conditions are backwards. You need to pick the Spawner_var=0 first, then pick a random one of those.