Final answer:
The question relates to property law, specifically regarding contingent remainders and the vesting of future interests. If A has no children, the property may likely become vested in B and his heirs upon A's death, in accordance with applicable laws and estate planning principles.
Step-by-step explanation:
The question seems to refer to a scenario involving property inheritance and legal entitlement based on conditions set forth in a will or trust. If property is granted to A for life, followed by A's children for their lives, and then to B and his heirs, but A has no children, this raises questions about contingent remainders and vesting of future interests in property law. Since A has no children at the time of the property grant, the interest meant for A's children is currently contingent—meaning it depends on a condition that has not yet been met (A having children). If A never has children, the property could then immediately become vested in B and his heirs upon A's death.
This scenario touches upon principles of estate planning, property rights, and inheritance law. It is also important to consider the impact of various laws and legal doctrines, such as the rule against perpetuities or terms of the trust or will, which might affect the ultimate disposition of the property. In modern legal practice, specific statutory provisions and case law would govern the eventual outcome.