<a id="a$id" onclick="check($id,1)" href="javascript:void(0)" class="black">Qualify</a>
After "href" is removed, is "Qualify" still clickable?
Your title question and your example are completely different. I'll start by answering the title question:
$("a").removeAttr("href");
And as far as not requiring an href, the generally accepted way of doing this is:
<a href"#" onclick="doWork(); return false;">link</a>
The return false is necessary so that the href doesn't actually go anywhere.