Changing from Subdomain to real domain

Today I bought a domain, changed DNS and all other settings. Domain worked right away after 1 minute.

It should be a simple question, but since I haven't done this before I will rather ask, before I do something what search engines won't like.

Previously I had a blogspot.com domain and now have chainged to a real .com domain. My question is how will Search engines see this change? Should I resubmit my new domain to all the search engines or should I rather leave it to avoid duplicate content?

I also have put my website to a few webdirectories and blog sites. Should I change the settings and update them to my new domain?

Thanks!

 

if you use 301 redirect from old domain to the new domain, you will not get any problem

 

I think that is what blogger does automatically, am I right or am I right?

 

I still am confused as to submit it or not? Will search engines recognize the new domain and automatically include it into their database?

 

just input your custom domain in blogspot settings and save . It will automatically do a 301 redirect and it will also save your page rank.

 

Excellent thanks. Reputation given.