Will google index my site which is created using a subdomain
my site is :

yes
get a google account
verify
(follow the instructions on google webmaster tools to get your site indexed) re links design
submit your sitemap online sitemap generator
do not join a link exchange, many are a negative effect on your page ranking

family.mysite.com
www.mysite.com
rent2own.mysite.com
in the google index

incidentally the script that says " we reccomend using firefox "
is wrong, this is not an IE browser at all, and not IE6,
Opera
you alienate many more of your visitors than you will get converts to another browser.
not a commercially viable idea.

As long as robots are not prohibited from searching your host, and as long as your homepage is named the name your host requires, the indexing should be automatic. Mine always appear within a day or two without any coaxing from me. I don't have to do anything, except upload the new pages and provide a link or a path of links that reaches from the homepage to the new pages.

I used to have a website on a host that prohibited robots. But because other people linked to my pages after I told them where they were, they also appeared on Google. I am amazed that some of them are still there, even though the site is now just a link site of the old urls with simple pages containing links to the new pages on my new site.

Midimagic is right, if the site is indexed at all
the googlebots pick up changes rapidly
my advice is if the site is completely new, and has no or limited external links

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