  We consider a class of asymptotic representations of the Borel subalgebra of
the quantum affine superalgebra U_q(gl(M|N)^). This is characterized by
Drinfeld rational fractions. In particular, we consider contractions of
U_q(gl(M|N)) in the FRT formulation and obtain explicit solutions of the graded
Yang-Baxter equation in terms of q-oscillator superalgebras. These solutions
correspond to L-operators for Baxter Q-operators. We also discuss an extension
of these representations to the ones for contracted algebras of U_q(gl(M|N)^)
by considering the action of renormalized generators of the other side of the
Borel subalgebra. We define model independent universal Q-operators as the
supertrace of the universal R-matrix and write universal T-operators in terms
of these Q-operators based on shift operators on the supercharacters. These
include our previous work on U_q(sl(2|1)^) case [arXiv:0805.4274] in part, and
also give a cue for the operator realization of our Wronskian-like formulas on
T-and Q-functions in [arXiv:0906.2039, arXiv:1109.5524].
