  We investigate how the Kondo screening cloud builds up as a function of space
and time. Starting from an impurity spin decoupled from the conduction band,
the Kondo coupling is switched on at time t=0. We work at the Toulouse point
where one can obtain exact analytical results for the ensuing spin dynamics at
both zero and nonzero temperature T. For t>0 the Kondo screening cloud starts
building up in the wake of the impurity spin being transported to infinity. In
this buildup process the impurity spin--conduction band spin susceptibility
shows a sharp light cone due to causality, while the corresponding correlation
function has a tail outside the light cone. At T=0 this tail has a power law
decay as a function of distance from the impurity, which we interpret as due to
initial entanglement in the Fermi sea.
