DCBH formation rate as a function of redshift for several halo masses and values of J_crit. The formation rate is normalized to the comoving volume of the main halo, where the red, green, and blue lines are for halo masses of 10¹¹ M_⊙, 10¹² M_⊙, and 10¹³ M_⊙, respectively. The solid, dashed, and dotted green lines show the numbers of DCBHs per redshift for J_crit = 100, 200, 400, respectively. The comoving volume is calculated as the mass of the main halo M_h divided by the average cosmic density. In all these cases, we can form DCBHs during the assembly of the halo. A larger halo mass and a lower value of J_crit facilitates the formation of a DCBH down to lower redshifts. In none of the cases can we form a DCBH at redshifts z < 7.3.