  We study the spreading of information in a wide class of quantum systems,
with variable-range interactions. We show that, after a quench, it generally
features a double structure, whose scaling laws are related to a set of
universal microscopic exponents that we determine. When the system supports
excitations with a finite maximum velocity, the spreading shows a twofold
ballistic behavior. While the correlation edge spreads with a velocity equal to
twice the maximum group velocity, the dominant correlation maxima propagate
with a different velocity that we derive. When the maximum group velocity
diverges, as realizable with long-range interactions, the correlation edge
features a slower-than-ballistic motion. The motion of the maxima is, instead,
either faster-than-ballistic, for gapless systems, or ballistic, for gapped
systems. The phenomenology that we unveil here provides a unified framework,
which encompasses existing experimental observations with ultracold atoms and
ions. It also paves the way to simple extensions of those experiments to
observe the structures we describe in their full generality.
