The present invention relates to a composition of branched fatty acids or esters thereof, the process for preparing such a composition and its use in various industrial fields, such as in lubricant, in cosmetics and in home care. More particularly, the present invention relates to a composition comprising at least 30% by weight of polybranched C10-C24 fatty acids or esters thereof, and a cyclic compound content ranging from 1% to 8% by weight, the weight percentage being given on the total weight of the composition.