We are interested in studying solutions to the non-local conservation law \(\partial _tu+\chi \partial _x(u\varLambda ^{\alpha -1}\mathcal {H}u)=0\) subject to initial data in \(u_0\in L^1\cap L^{\infty }\) , where \(\chi =\pm 1\) . We proved that there is a finite existence time \(T^{*}\) (maximal time) such that the solution u is finite in \([0,T^{*})\) and blows up at \(T^{*}\) in the sense of mass concentration \((\chi =-1)\) . We proved that in the case \(\chi =1\) the solution exhibits a spreading of the initial datum, which is verified via numerical insights. We also improved comprehension of the results of Biler and Karch (J. Evol. Equ. 10:247–262, 2010) and Li and Zhang (Commun. Pure Appl. Anal. 9(6):1591–1606, 2010) to simplify the analysis and to circumvent the requirement of initial concentration such that our results hold for initial data in \(L^1\cap L^{\infty }\) .