Bollobas　and　Scott　showed　that　the　vertices　of　a　graph　of　m　edges　can　be　partitioned　into　k　sets　such　that　each　set　contains　at　most　m/k(2)　o(m)　edges.　They　conjectured　that　the　vertices　of　an　r-uniform　hypergraph,　where　r　＞　3,　of　m　edges　may　likewise　be　partitioned　into　k　sets　such　that　each　set　contains　at　most　m/kr　o(m)　edges.　In　this　paper,　we　prove　the　weaker　statement　that　a　partition　into　k　sets　can　be　found　in　which　each　set　contains　at　most　m/(k-1)(r)+r(1/2)　+o(m)　edges.　Some　partial　results　on　this　conjecture　are　also　given.　(C)　2016　Elsevier　Inc.　All　rights　reserved.