The process you are describing is known as asexual reproduction through spore formation or simply spore formation. In this process, fungi, algae, and some plants produce reproductive cells called spores that are capable of developing into new individuals without the need for fertilization.
In fungi, for example, these spores can be produced through structures like sporangia or can be released as conidia. Similarly, in certain algae and plants, fragments of the organism or specialized structures can lead to the formation of spores, which can germinate and grow into new organisms, allowing for rapid population growth in suitable conditions.