  The diameter of the apparent horizon, defined by the distance between
furthest points on the horizon, in spacetimes with a positive cosmological
constant $\varLambda$ has been investigated. It is established that the
diameter of the apparent horizon on the totally umbilic partial Cauchy surface
cannot exceed $2\pi/\sqrt{3\varLambda}$. Then, it is argued that arbitrarily
long black strings cannot be formed in our universe.
