My husband died without a will. Our home has his name on the deed. He has two children from a past relationship. What are the children entitled to?

If your name is on the deed as well, as husband and wife or as joint tenants, the house is now yours.  Otherwise, the house is part of his estate.

Under New Jersey's intestate succession statutes, your share of your husband's estate is the first 25% of the estate, up to $200,000 but not less than $50,000, and one-half of the rest, with the other half-of-the-rest going to his children in equal shares.  If the house is part of the estate, the equity as of the date of death is its value, for this calculation.

I'd recommend hiring a local attorney to help you probate your late husband's estate, and especially so if there's any chance the net estate will be more than $50,000, or if his children are or might be hostile to you, and absolutely if both of those are true.