Fragmentation of massive dense molecular clouds is the starting point in the formation of rich clusters and massive stars. Theory and numerical simulations indicate that the population of the fragments (number, mass, diameter, separation) resulting from the gravitational collapse of such clumps is probably regulated by the balance between the magnetic field and the other competitors of self-gravity, in particular turbulence and protostellar feedback. We have observed 11 massive, dense and young star-forming clumps with the Atacama Large Millimeter Array (ALMA) in the thermal dust continuum emission at $sim 1$~mm with an angular resolution of 0.25 arcseconds with the aim of determining their population of fragments. We find fragments on sub-arcsecond scales in 8 out of the 11 sources. The ALMA images indicate two different fragmentation modes: a dominant fragment surrounded by companions with much smaller mass and size, and many ($geq 8$) fragments with a gradual change in masses and sizes. On average, the largest number of fragments is found towards the warmer and more massive clumps. Also, the warmer clumps tend to form fragments with larger mass and size. To understand the role of the different physical parameters to regulate the final population of the fragments, we have simulated the collapse of a massive clump of $100$ and $300$ M$_{odot}$ having different magnetic support. The simulations indicate that: (1) fragmentation is inhibited when the initial turbulence is low, independent of the other physical parameters. (2) a filamentary distribution of the fragments is favoured in a highly magnetised clump. We conclude that the clumps that show many fragments distributed in a filamentary-like structure are likely characterised by a strong magnetic field, while the others are possible also in a weaker magnetic field.
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