  Molecular clouds are the most important incubators of young stars clustered
in various stellar structures whose spatial extension can vary from a few AU to
several thousand AU. Although the reality of these stellar systems has been
established, the physical origin of their multiplicity remains an open
question. Our aim was to characterise these stellar groups at the onset of
their formation by quantifying both the number of stars they contain and their
mass using a hierarchical fragmentation model of the natal molecular cloud. We
developed a stochastic and predictive model that reconciles the continuous
multi-scale structure of a fragmenting molecular cloud with the discrete nature
of the stars that are the products of this fragmentation. This model was
implemented within a gravo-turbulent fragmentation framework to analytically
follow the fragmentation properties along spatial scales using an isothermal
and adiabatic equations of state (EOSs). Using an adiabatic EOS we determined a
characteristic spatial scale where further fragmentation is prevented, around a
few tens of AU. We show that fragmentation is a self-regulated process as
fragments tend to become marginally unstable following a $M \propto R$
Bonnor-Ebert-like mass-size profile. Supersonic turbulent fragmentation
structures the cloud down to $R \approx 0.1$ pc, and gradually turns into a
less productive Jeans-type fragmentation under subsonic conditions so
hierarchical fragmentation is a scale dependant process. Our work suggests that
pre-stellar objects resulting from gas fragmentation, have to progressively
increase their accretion rate in order to form stars. A hierarchical
fragmentation scenario is compatible with both the multiplicity of stellar
systems identified in Taurus and the multi-scale structure extracted within NGC
2264 molecular cloud.
