The horizonatally growing hyphae of Rhizopus are called

Rhizoids are thread-like structures that anchor the fungus to the substrate. They are not involved in reproduction.

Sporangiophores are upright hyphae that bear sporangia. Sporangia are structures that produce spores.

Holdfasts are structures that anchor the fungus to a substrate in aquatic environments. They are not found in Rhizopus.