In this paper we present a decentralized abstraction framework for multiagent systems with couplings in their dynamics, which arise in their popular coordination protocols. The discrete models are basexl on a varying decentralization degree, namely, the agents' individual abstractions are obtained by using discrete information up to a tunable distance in their network graph. Deriving these models at the agent level is essential to address scalability issues which appear in the discretization of systems with a high state dimension. The approach builds on the appropriate discretization of the agents' state space and the selection of a transition time step, which enable the construction of a nonblocking transition system for each agent with quantifiable transition possibilities. The transitions are based on the design of local feedback laws for the manipulation of the coupling terms, which guarantee the execution of the transitions by the continuous systems. For a class of nonlinear agent interconnections, the derivation of such abstractions is always guaranteed, based on sufficient conditions which relate the agents' dynamics and the space/time quantization.