Traditionally paired with impulsive communications, Time-Hopping CDMA (TH-CDMA) is a multiple access technique that separates users in time by coding their transmissions into pulses occupying a subset of $N_\mathsf{s}$ chips out of the total $N$ included in a symbol period, in contrast with traditional Direct-Sequence CDMA (DS-CDMA) where $N_\mathsf{s}=N$. This work analyzes TH-CDMA with random spreading, by determining whether peculiar theoretical limits are identifiable, with both optimal and sub-optimal receiver structures, in particular in the archetypal case of sparse spreading, that is, $N_\mathsf{s}=1$. Results indicate that TH-CDMA has a fundamentally different behavior than DS-CDMA, where the crucial role played by energy concentration, typical of time-hopping, directly relates with its intrinsic "uneven" use of degrees of freedom.