In many cases, your parents will have a trust or other legal document in place that prevents the family home from entering into probate when they die. It's not often that both parents die at the same time, but it isn't out of the realm of possibility for it to happen. If for some reason nothing was set up properly, you will need to follow the local procedure for transferring the deed of the home through probate.
It's important to know that a will and a trust are two very different legal documents. A will simply explains the wishes of a person after they die. A trust helps move property from one person to another after death by avoiding probate. When you draft a trust, you move property without paying taxes on it.
You need to do a little research when your parents die. This includes taking a look at the deed that has their names on it. The deed could be joint tenancy, quitclaim, grant or a warranty deed. The deed will state how your parents held the property. This same information should explain how you will be able to hold the property once the deed is transferred to you.
There might not be a way to avoid probate if the home was owned solely by one of your parents. Even if a will was present, and it states who is to get the home, it will likely still need to go through probate.
Transferring a deed to a home through probate can be a stressful process. Make sure you consult with an experienced attorney when in such a situation. This is not something you want to try on your own, as you could risk making a serious mistake.