Context : Multiple systems are the product of protostellar core fragmentation . Studying their statistical properties in young stellar populations therefore probes the physical processes at play during star formation . Aims : Our project endeavors to obtain a robust view of multiplicity among embedded Class I and Flat Spectrum protostars in a wide array of nearby molecular clouds to disentangle “ universal ” from cloud-dependent processes . Methods : We have used near-infrared adaptive optics observations at the VLT through the H , K _ { s } and L ^ { \prime } filters to search for tight companions to 45 Class I and Flat Spectrum protostars located in 4 different molecular clouds ( Taurus-Auriga , Ophiuchus , Serpens and L1641 in Orion ) . We complemented these observations with published high-resolution surveys of 13 additional objects in Taurus and Ophiuchus . Results : We found multiplicity rates of 32 \pm 6 % and 47 \pm 8 % over the 45–1400 AU and 14–1400 AU separation ranges , respectively . These rates are in excellent agreement with those previously found among T Tauri stars in Taurus and Ophiuchus , and represent an excess of a factor \sim 1.7 over the multiplicity rate of solar-type field stars . We found no non-hierarchical triple systems , nor any quadruple or higher-order systems . No significant cloud-to-cloud difference has been found , except for the fact that all companions to low-mass Orion protostars are found within 100 AU of their primaries whereas companions found in other clouds span the whole range probed here . Conclusions : Based on this survey , we conclude that core fragmentation always yields a high initial multiplicity rate , even in giant molecular clouds such as the Orion cloud or in clustered stellar populations as in Serpens , in contrast with predictions of numerical simulations . The lower multiplicity rate observed in clustered Class II and Class III populations can be accounted for by a universal set of properties for young systems and subsequent ejections through close encounters with unrelated cluster members .