The type of reproduction in which offspring form on the surface of the parent is called budding. In this process, a new organism develops from an outgrowth or bud on the parent organism. This method is commonly seen in organisms such as yeast and some types of hydra.
Here's a brief overview of the other terms you mentioned:
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Fragmentation: This is a form of asexual reproduction where an organism is broken into fragments, and each fragment can develop into a new organism. This is seen in some starfish and worms.
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Binary fission: This is a method of asexual reproduction common in prokaryotes (like bacteria), where the parent organism divides into two approximately equal parts, each becoming a new organism.
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Vegetative reproduction: This is a method of asexual reproduction in plants where new individuals grow from a fragment of the parent plant (like tubers or runners).
In summary, the correct answer to your question is budding.