To solve sparse systems of linear equations, multifrontal methods rely on dense partial LU decompositions of so-called frontal matrices; we consider a parallel asynchronous setting in which several frontal matrices can be factored simultaneously.In this context, to address performance and scalability issues of acyclic pipelined asynchronous factorization kernels, we study models to revisit properties of left and right-looking variants of partial \(LU\) decompositions, study the use of several levels of blocking, before focusing on communication issues.The general purpose sparse solver MUMPS has been modified to implement the proposed algorithms and confirm the properties demonstrated by the models.