Promotion of site on free domain

[cricketmania]

Hi all,
I have a site hosted on a free domain. I want to know whether I have to restart the promotion process if I register a new domain and shift my shift to it.
How can I change my listing in Dmoz and google. (or do I need to submit the site again).
What about the link exchange sites.

Thanks in advance for your help.
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[cbp]

How can I change my listing in Dmoz and google. (or do I need to submit the site again).

Just click on the update url link on the page at DMOZ - then wait patiently for it to be changed - check at www.resource-zone.com after a month of submitting the update url to make sure they received it.

CBP