A study reported by the BBC (H/T Jason Malloy) found that, contrary to expectations, tall men do not have the most children. Men of average height do.
I replicated the study with MIDUS data on 2,316 white men, and found the following:
Mean number of children
Tall men 2.43
Average men 2.57
Short men 2.46
The results are similar to the study's (the numbers are high because stepchildren and adopted children are included). The difference is attributed to average men marrying earlier. The thinking seems to be that taller men hold out longer before getting married--because of greater attractiveness--and end up marrying women who are also older and who have fewer married years in which to have children.