Assuming there is no Will in place which excludes the child from the parents estate, and depending on the existence of other parties with interests in the estate [i.e..brothers,sisters, others ] the distribution of the deceased's assets is dealt with by the intestacy law of the state in which the deceased dies and the estate is opened.
The rules of "descent and distribution" (which is the terminology used to describe the process by which property passes when there is no Will), vary from state to state and are based upon state, not federal, law. These rules outline the rank order of persons (heirs) who have a claim to the estate, and the process by which creditors of the deceased can make claims against the assets. In that regard, the heirs are generally not personally liable liable for the payment of the deceased's debts (unless they contracted for that liability), but a valid claim of a creditor properly and timely made, can deplete the assets of the estate such that there is less to distribute to the heirs.
The child will have to file his/her claim with the court/trustee/administrator/attorney handling the estate. States have separate courts that deal with probate-sometimes called "Probate Courts", and sometimes known by another name.
The ultimate amount that a child will receive will depend upon factors such as the total amount of assets in the estate, the number of beneficiaries and the nature of their relationship to the deceased (for example, a surviving spouse often gets the bulk of the estate) attorney's fees, and court costs. In larger and more complex estates, accountant's fees may become an issue, as would taxes of various sorts.
Canada
Normally a probate Count would put the properties of the deceased in the trust of an adult, usually a family member of the children until the children come of age and can inherit the property.
United States
You need to provide more details for an accurate answer. The following is a sampling of what may happen under various circumstances:
You can check the laws in your state at the related question link provided below.
Muslim Law
Muslim Law based on Quran gives fixed share of ¼ to husband and 1/8 for wife/wives when they have children. The remaining share going to children, single daughter getting ½ or 2/3 if they are more, having no brother. In case of brother the sisters share with them; 2 shares for boys and one share for girl
The solely owned property of a person who dies without a will passes as intestate property according to the state laws of intestacy. Each state has its own scheme. You can check the laws in your particular state at the related question link provided below.
As for any property the decedent owned with another person, it depends on how title was held. Title to property held as joint tenants passes directly to the surviving joint tenant. You should consult with an attorney who specializes in probate who can review your situation and explain your rights, if any.
Part of it will depend on if the child is a minor. If they are an adult, there isn't much that can be done about it. A minor's guardian can claim a portion of the estate.
It depends if there was a will or not. Step-children have no rights to the estate of a step-parent unless specifically named in the will. If there was no will, the estate is typically divided between the spouse and the children. Check the laws for your state or jurisdiction.
Not if the other parent has joint custody and/or visitation rights.
Why should adult children have any rights to the personal gains of a parent, unless they worked to add to them?
You will have to consult the intestacy laws for the state involved. Usually there is a rule that the estate is split evenly and the spouse gets half and the children get half. Consult a probate attorney in your jurisdiction.
Biological and legally adopted children generally have the same rights in their parent's estate if their parent dies intestate, or, without a will. Children do not inherit an interest in property that was held jointly with a surviving spouse. However, they may inherit an interest in property held solely by the decedent. You can check the laws of intestacy in your state in the related question below.
The debts of the parents are paid by the parent's estate, not their children.
The children share equally in the estate. If there are any children who predeceased the last parent to die and if those children left children of their own, then those grandchildren would inherit the share that their parent would have inherited and he/she not predeceased.
If there is no will, most states distribute the assets that way. You would have to look at the specific probate laws for the state in question. And if there is a will the estate will be distributed according to the wishes of the decedent. If the children from a previous marriage are minors, the court may over ride the will to prevent them from becoming wards of the state.
Not sure if the same applies worldwide but certainly not in the UK
You mean a contract to sell a property in which the parent has a life estate? No. If the children want to sell their future interest in the property, it is separate from the rights of the parent with a life estate. Similarly, the children do not need to be asked if the the parent wants to sell (or mortgage) his or her life estate to someone else. On the other hand, if the buyers want clear title, with no life estate, then you have a different problem: terminating the life estate, by merging it with the future estate, and what's in it for you?
It will be distributed according to the intestacy laws of the state. In most cases there isn't an issue with that, as the children will inherit. And the children can open an estate regardless if there is a will or not.
The parent's estate is responsible for their debts. If there is no estate the creditors are out of luck. However, if the parent left any assets, the estate must be probated in order to give creditors an opportunity to file a claim.