The kilometer size barrier is a term given to a barrier on planet formation beyond a size of on the order of a kilometer in diameter. Planet-formation theories attempt to explain their development from collections of dust into larger and larger bodies, to asteroid or planet size. Multiple problems remain in current explanations of such a phenomenon, some of the individual problems identified by the size of the object for which further growth seems impeded.
The kilometer size barrier is specifically: at (very) roughly a kilometer in diameter, there are expected to be planetesimal collisions with sufficiently high relative velocity that their material would be scattered, setting back the process and placing a limit on the growth.
Other "barriers" include the "charging barrier", the "bouncing barrier", and the meter size barrier.
The kilometer size barrier was theorized in 2009 by Ida et al.