In the past decade, there has been an increasing interest in the study of (maximal) almost disjoint families of countable vector spaces, along with mad families of subspaces satisfying certain properties. In this talk, we consider the direct analogue of complete separability for mad families of subspaces. Completely separable mad families of subsets of N have been studied for over 30 years since their introduction by Balcar and Simon. While recent works by Shelah and Mildenberger-Raghavan-Steprāns show that one can construct a completely separable MAD family under extremely weak set-theoretic hypotheses, it remains unknown whether such a construction is possible in ZFC. In this talk, we discuss the construction of a completely separable MAD family (of subsets of N) by Mildenberger-Raghavan-Steprāns, and apply it to show that there is a completely separable mad family of subspaces in ZFC.