  We study the spreading of excitations in 2D systems of mobile agents where
the excitation is transmitted when a quiescent agent keeps contact with an
excited one during a non-vanishing time. We show that the steady states
strongly depend on the spatial agent dynamics. Moreover, the coupling between
exposition time ($\omega$) and agent-agent contact rate (CR) becomes crucial to
understand the excitation dynamics, which exhibits three regimes with CR: no
excitation for low CR, an excited regime in which the number of quiescent
agents (S) is inversely proportional to CR, and for high CR, a novel third
regime, model dependent, here S scales with an exponent $\xi -1$, with $\xi$
being the scaling exponent of $\omega$ with CR.
