That is indeed the case, you can fully legally do anything you wish with your assets in death, including giving it to one child (or pet). Granted, it's also not unusual for lawsuits to fly if you leave everything to one child rather than spreading it out. That happens from time to time with the super wealthy in cases of feuding.

In the US it became custom to more or less equally distribute assets in death to all of the children, rather than concentrating it to one controlling heir. That's still the overwhelmingly common custom to this day.