  We present a new implementation of the tracer particles algorithm based on a
Monte Carlo approach for the Eulerian adaptive mesh refinement code Ramses. The
purpose of tracer particles is to keep track of where fluid elements originate
in Eulerian mesh codes, so as to follow their Lagrangian trajectories and
re-processing history. We provide a comparison to the more commonly used
velocity-based tracer particles, and show that the Monte Carlo approach
reproduces the gas distribution much more accurately. We present a detailed
statistical analysis of the properties of the distribution of tracer particles
in the gas and report that it follows a Poisson law. We extend these Monte
Carlo gas tracer particles to tracer particles for the stars and black holes,
so that they can exchange mass back and forth between themselves. With such a
scheme, we can follow the full cycle of baryons, that is, from gas-forming
stars to the release of mass back to the surrounding gas multiple times, or
accretion of gas onto black holes. The overall impact on computation time is
$\sim$ 3% per tracer per initial cell. As a proof of concept, we study an
astrophysical science case -- the dual accretion modes of galaxies at high
redshifts --, which highlights how the scheme yields information hitherto
unavailable. These tracer particles will allow us to study complex
astrophysical systems where both efficiency of shock-capturing Godunov schemes
and a Lagrangian follow-up of the fluid are required simultaneously.
