We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of R-N with Dirichlet boundary conditions. We analyze the controllability problem with distributed controls ( supported on a small open subset) and boundary controls ( supported on a small part of the boundary). We prove that the system is null and approximately controllable at any time if the nonlinear term f (y, dely) grows slower than |y| log(3/2) (1 + |y| + |dely |) + |dely | log(1/2) (1 + | y | + |dely |) at infinity ( generally, in this case, in the absence of control, blow-up occurs). The proofs use global Carleman estimates, parabolic regularity, and the fixed point method.