Let [Mscr ]S be the universal maximal operator over unit vectors of arbitrary directions. This operator is not bounded in L2(R2). We consider a sequence of operators over sets of finite equidistributed directions converging to [Mscr ]S. We provide a new proof of N. Katz's bound for such operators. As a corollary, we deduce that [Mscr ]S is bounded from some subsets of L2 to L2. These subsets are composed of positive functions whose Fourier transforms have a logarithmic decay or which are supported on a disc.