  We consider the phase transition in the system of n simultaneously developing
random walks on the halfline x>=0. All walks are independent on each others in
all points except the origin x=0, where the point well is located. The well
depth depends on the number of particles simultaneously staying at x=0. We
consider the limit n>>1 and show that if the depth growth faster than 3/2 n
ln(n) with n, then all random walks become localized simultaneously at the
origin. In conclusion we discuss the connection of that problem with the phase
transition in the copolymer chain with quenched random sequence of monomers
considered in the frameworks of replica approach.
