Theoretical variations in the fragmentation rate φ (a), the mean fragment density 〈ρ〉 (b) as a function of the spatial scale R for different mass transfer rates ξ. These profiles were computed using an adiabatic EOS (c), a cloud initial size R₀ = 10 pc with an initial density ρ₀ = 10⁻²¹ g/cm³. Red triangle, black dot, blue triangle, and blue square indicate the position of the last fragmenting structures for mass transfer rates ξ = 1,0.5,0, −0.5, −1, respectively. (a) The black dotted line is associated with an isothermal EOS with a polytropic index p = 1. The transition between turbulent and thermal fragmentation is delimited by the grey line. (b) The black dashed line indicates the density of the first Larson core (Larson 1969) when p = 5/3. (c) Evolution of temperature T as a function of fragments density.