|Do most children with autism have their vaxes?
Yes, in the US. So do most children who don't have autism.
The correlation between vaccination (mostly on thimerisol in vaccines) and autism has been studied pretty closely. The studies
seem to indicate that there is no correlation - vaccinated children don't develop the syndrome any more (or less) than un-vaccinated.
Many diagnoses of autism tend to be made in childhood, childhood is when most children are vaccinated, therefore it often seems that symptoms of autism appear after a vaccination. Plus there is a lot of attention paid to the possibility of a link, and therefore parents often make the association based on that.
But essentially there is no significant evidence to indicate that vaccination causes autism.