According to news reports, Prince died without a will. The probate court has appointed a bank to administer his estate. Several persons have claimed to be his children: DNA testing is being done.
If no valid will is found, the laws of his State will determine who inherits. If he had any children, they will inherit, and his siblings will receive nothing. If he had no children, his estate will be divided among his siblings, with full and half brothers and sisters being treated equally.
Although it is possible that everyone will cooperate, we may also see years of nasty court battles ahead. Given the size of his Estate, it is virtually certain that they will end up paying a lot more in taxes than they would had some basic estate planning been performed.
We may never know what he would have wanted to happen. All of this uncertainty could have been avoided had he gone to his attorneys and executed a will. This would, among other things, allowed Prince to decide who would be in control of his music, and to specify who should inherit his money.