A probate needs to be open. Your sister's statement that the State will take half if a probate is opened is completely false. You should hire an attorney to open the probate to take care of creditors claims and to properly distribute the estate assets. Once the probate is open, the attorney should be able to get any information regarding your father's assets and determine how they are to be distributed.
See this is precisely the problem with trying to get legal advice from family members - unless they are lawyers, the advice you get will most often be completely and totally bogus. Nothing escheats to the state unless there are no heirs. Period. If Mom is still living, and she was still married to Dad when he passed, and the children share the same ancestry, then Mom will get the estate. If Dad had children with another woman (earlier marriage?) then they will take 50% of the estate. Regardless, the estate needs to be probated to take care of taxes, creditors of the estate, and to transfer title to properties. Seek the advice of a good probate attorney. In FL, by law, you MUST have an attorney file the probate proceeding. Good luck.
My answer is of a general nature and should not be construed to be legal advice nor creating an attorney-client relationship. Carol Johnson Law Firm, P.A. practices in the area of Wills, Trusts, and Estates, Disability - with a particular focus on providing Special Needs Trusts for disabled children and adults.
If a person does not have a will their assets will typically pass pursuant to the laws if intestate succession. These laws vary from state to state. But the laws usually dictate as to how the person property will pass. Also if the account is a joint account it will possibly pass to the co-owner on that account. Your mother may also be entitled to a certain amount of an exemption to that property as the living spouse. Some states have inheritance taxes that apply to estates at death, but there are also certain exemptions as well. You probably should consult a probate attorney in the state that your father was living in at the time of his death.
Your question does not make clear where your father was residing at the time of his death. Whatever your father inherited that was owned in his name alone or, if jointly owned, does not have a survivorship interest or does not have a beneficiary designation would be part of his probate estate and would be subject to distribution under the terms of his will or under the laws of intestacy if he had no will. I suggest that you confer with an attorney in the county in which your father was residing at the time of his death. I do not think you will be able to resolve this on your own. Also, the state does not take assets if the estate does through probate unless there are no known heirs/beneficiaries. That bit of information is nothing more than "urban legend."