On effective descent $\mathcal V$-functors and familial descent morphisms

We study effective descent $\mathcal V$-functors for cartesian monoidal categories $\mathcal V$ with finite limits. This study is carried out via the properties enjoyed by the $2$-functor $\mathcal V \mapsto \mathsf{Fam}(\mathcal V)$, results about effective descent of bilimits of categories, and the fact that the enrichment $2$-functor preserves certain bilimits. Since these results rely on an understanding of (effective) descent morphisms in $\mathsf{Fam}(\mathcal V)$, we briefly study those epimorphisms when $\mathcal V$ is a regular category.