Herein, we present an analytic length distribution of vapor-liquid-solid nanowires growing without the nucleation delays of the very first monolayer, by the direct impingement of material from vapor, and in the absence of desorption. We show that nucleation antibunching narrows the Poissonian length distribution to a time-independent asymptotic shape. The obtained distribution depends on the sole control parameter epsilon describing the effect of antibunching, and has a variance of 1/(2 epsilon) rather than spreading infinitely with time. A good agreement is found between the analytic shapes obtained within the continuum growth theory and Green's function of the discrete rate equations describing the length statistics of nanowires. Overall, this narrowing effect can be used to improve the size homogeneity of III-V and other semiconductor nanowires grown under the appropriate conditions.