Final answer:
The type of cell division in asexually reproducing organisms that results in offspring genetically identical to the parents is known as mitosis.
Step-by-step explanation:
Asexually reproducing organisms produce offspring that are genetically identical to each other and the parents. This type of cell division is known as mitosis. It involves the replication of a single parent's genetic material into two daughter cells. Asexual reproduction methods such as binary fission, fragmentation, and budding all rely on mitosis to produce clones of the parent organism. Unlike meiosis, which leads to genetic variation in sexually reproducing organisms, mitosis ensures that the offspring are exact genetic copies of the parent, which is characteristic of asexual reproduction.
It's important to note that while sexual reproduction through meiosis introduces variation into offspring, asexual reproduction through mitosis does not. Sexual reproduction involves two parents and the process of fertilization, leading to offspring that are not genetically identical to the parents, unlike asexual reproduction.
In contrast to mitosis, crossing over is a process that occurs during meiosis and aids in genetic recombination, and fertilization is the union of two haploid gametes to form a zygote. Therefore, the correct answer to the question is B. Mitosis.