What process involves a mother cell producing buds?

The process that involves a mother cell producing buds is known as budding. In this type of asexual reproduction, a new organism develops from an outgrowth or bud on the parent. This bud receives nourishment from the parent while it develops, and once it matures, it can separate and live independently. This is a common reproductive strategy seen in various organisms, including yeasts and some types of protozoa.

Budding differs from other reproductive processes such as fragmentation, where an organism breaks into pieces that can each grow into a new individual. In binary fission, a single cell divides into two identical cells, which is common in prokaryotic organisms like bacteria. Asexual reproduction is a broader category that includes budding, fragmentation, and binary fission, but it does not specifically define the process of producing buds, making budding the most precise answer in this context.