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We study the convergence of $N-$particle systems described by SDEs driven byBrownian motion and Poisson random measure, where the coefficients depend onthe empirical measure of the system. Every particle jumps with a jump ratedepending on its position and on the empirical measure of the system. Jumps aresimultaneous, that is, at each jump time, all particles of the system areaffected by this jump and receive a random jump height that is centred andscaled in $N^{-1/2}.$ This particular scaling implies that the limit of theempirical measures of the system is random, describing the conditionaldistribution of one particle in the limit system. We call such limits {\itconditional McKean-Vlasov limits}. The conditioning in the limit measurereflects the dependencies between coexisting particles in the limit system suchthat we are dealing with a {\it conditional propagation of chaos property}. Asa consequence of the scaling in $N^{-1/2}$ and of the fact that the limit ofthe empirical measures is not deterministic the limit system turns out to besolution of a non-linear SDE, where not independent martingale measures andwhite noises appear having an intensity that depends on the conditional law ofthe process.

White-noise driven conditional McKean-Vlasov limits for systems of particles with simultaneous and random jumps