What will happen if my father passed away with no Will and no beneficiary on neither his life insurance or retirement fund?

I am so sorry for your loss.  Are they your half siblings through your Father or step siblings?  How they are treated under the law for probate are very different and more facts are needed here.  If they are also children of your Father then they are entitled to receive inheritance that does not pass to your Mother automatically under the law either by joint ownership or beneficiary designation and if the property is designated as community property or separate property under the law.  No Will means that he died "intestate" and the intestacy laws in your state will apply.  All property acquired during a marriage is presumed to be community property. Under Texas laws, if you are married and are survived by a spouse and children, then your surviving spouse will inherit all your community property if all your children are also the children of your surviving spouse. Otherwise, all your one-half interest in the community estate will pass to your children, with your spouse keeping only his or her one-half interest. If your property is characterized as separate property, the distribution scheme is different. If you are survived a spouse and children, your surviving spouse is entitled to one third of your separate personal property and only a life estate (the right to use the property until his or her death) in one-third of your separate real property. The rest would be inherited outright by the children of the deceased spouse. I believe that the portion of the retirement funds that accrued during the marriage would be Mom's and the rest would be considered separate property for distribution under the intestacy statute, which means you would receive a portion of the funds.  I would speak with a lawyer in your area.  Good luck.