Good question. I am actually not super familiar with it, but in general your shares are owned under the name of the broker (called "street name"). That broker will then deal with portioning out dividends etc. I believe you can request to have personal ownership assigned, but this is expensive from what I have read. Unless you don't trust your broker (why are you using them?) it is unlikely to matter to an individual investor. You still have the legal right to the shares.

There exist also registered shares[1] for wich each owner of a share is registered in a shareholder register.

[1] https://en.m.wikipedia.org/wiki/Registered_share

Well, it would be stupid to trust the broker. What technically prevents them to run away with all stocks? I currently manage it by simply having accounts with several to avoid putting all eggs in one basket. But this is hardly a solution.

That is where your personal judgement comes in of course, but it would be hard for them to "run away with the stocks". These are not physical certificates, but just registrations in a central organisation.

Brokers (in traditional finance) are regulated, audited, and also are often subject to insurance policies in case they went bankrupt, or similar. If you are dealing with a large and reputable institution, you are unlikely to gain any benefit by assigning the shares to yourself I would suspect. Someone please correct me if I am missing something though.

What prevents them is custody. Funds, brokers, etc. are all required to use custody providers to keep track of assets and handle the actual transfer of assets.

> What technically prevents them to run away with all stocks?

It's called the law.

> Well, it would be stupid to trust the broker. [..] I currently manage it by simply having accounts with several[...]

If you believe it's "stupid" to trust brokers, spreading your exposure across several of them may protect against a complete loss. But it also increases the risk of some loss and, on balance, has exactly the same expected value. The law diminishing marginal utility may put your strategy slightly ahead, but the difference is similarly marginal.

> What technically prevents them to run away with all stocks?

SIPC insurance is supposed to protect you in case they run away anyway.

>What technically prevents them to run away with all stocks?

What protects a bank from running away with your cash?