Does enlarged adenoids in children cause asthsma?

No. Asthma has a complex origin in genetic and environmental triggers. Kids with enlarged adenoids are often sicker than others for a number of reasons, but the presence of the enlargement does not cause asthma.
Adenoids... ...Can be enlarged by the same mechanism as causes asthma (hypersensitivity, ) but though they may be related, it's more as "siblings, " not "parent and child.".