  In this paper, we introduce a new scale of tent spaces which covers, the
(weighted) tent spaces of Coifman-Meyer-Stein and of
Hofmann-Mayboroda-McIntosh, and some other tent spaces considered by Dahlberg,
Kenig-Pipher and Auscher-Axelsson in elliptic equations. The strong
factorizations within our tent spaces, with applications to quasi-Banach
complex interpolation and to multiplier-duality theory, are established. This
way, we unify and extend the corresponding results obtained by
Coifman-Meyer-Stein, Cohn-Verbitsky and Hyt\"onen-Ros\'en.
