  For any commutative algebra $R$ the shuffle product on the tensor module
$T(R)$ can be deformed to a new product. It is called the quasi-shuffle
algebra, or stuffle algebra, and denoted $T^q(R)$. We show that if $R$ is the
polynomial algebra, then $T^q(R)$ is free for some algebraic structure called
Commutative TriDendriform (CTD-algebras). This result is part of a structure
theorem for CTD-bialgebras which are associative as coalgebras and whose
primitive part is commutative. In other words, there is a good triple of
operads $(As, CTD, Com)$ analogous to $(Com, As, Lie)$.
