We introduce a functor from the category of braided spaces into the category of braided Hopf algebras which associates to a braided space V a braided Hopf algebra of planar rooted trees H P,R(V) . We show that the Nichols algebra of V is a subquotient of H P,R(V) . We construct a Hopf pairing between H P,R(V) and H P,R(V ∗) , generalising one of the results of [Bull. Sci. Math. 126 (2002) 193–239]. When the braiding of c is given by c( v i ⊗ v j )= q i, j v j ⊗ v i , we obtain a quantification of the Hopf algebras H D P,R introduced in [Bull. Sci. Math. 126 (2002) 193–239; 126 (2002) 249–288]. When q i, j = q a i, j , with q an indeterminate and ( a i, j ) i, j the Cartan matrix of a semi-simple Lie algebra g , then U q( g +) is a subquotient of H P,R(V) . In this case, we construct the crossed product of H P,R(V) with a torus and then the Drinfel'd quantum double D( H P,R(V)) of this Hopf algebra. We show that U q( g) is a subquotient of D( H P,R(V)) .