Is the headline given to this Thorax paper by the BBC, which also reports that the association was even stronger in children who had two parents with allergies.
The study is: well, I can't actually find it in Thorax, or anywhere else, so perhaps the BBC (and all the other media sources that appear in a search of G**gle for the author's name and the word "asthma") have got an advance copy.
I will try to come back to this another day and fill in the gaps. Meanwhile if you can find the Thorax paper, leave me a comment. Especially if I have missed it.