The short answer is YES. If your husband dies intestate, that is, without a will or a trust which specifically devises his property, the state of Florida says that you would take half of his estate and his adult children (assuming from your question that they are from another marriage) would share the other half. For a more detailed response or to explore other options, please feel free to contact me.
Yes its possible for the items that are not jointly owned nor covered by a will. The easy way to resolve this issue is to jointly title all assets, and have a will or trust to deal with the remaining assets. You and your husband may need separate attorneys for this to make sure and avoid a future will contest or claims by the children. Either way you should have a Florida Estate Planning Lawyer review your objectives and assets to give you the various options on how to preserve your interest in the property and do what you want upon your incapacity or death with your assets.
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I agree with the first two responses. Although sometimes difficult, it is much easier to deal with these issues know while you are both living than wish you would have. Your husband may want to preserve assets for you durin your life with the balance going to his children on your death; you may want to do the same thing if you have children from a prior marriage (i.e. provide for your husband if he survives but ultimately have the assets pass to your children, not his). Seek the advice of estate planning counsel. Good luck.
Mr. Post is licensed to practice law in KS and MO. The response herein is not legal advice and does not create an attorney/ client relationship. The response is in the form of legal education and is intended to provide general information about the matter within the question. Oftentimes the question does not include significant and important facts and timelines that if known could significantly change the reply unsuitable. Mr. Post strongly advises the questioner to confer with an attorney in their state in order to ensure proper advice is received.