I'm asking this because I need to buy a few sites and I need to move them to my host. This means IP change. I'm also thinking about transferring the domain to my preferred registrar.

How do these things reflect on already established PageRank and SEO authority:
1. IP change
2. Domain registrar change

What is the best thing to do?

Page rank will be transferred to your new host there will be no problem in that. Just for few days you may lose keyword rankings but they will be up automatically.

Agree with the previous reply. You will easily get the page rank back. The ranking might be affected.

if you follow the rules , there will be no problems transfering your page rank.

Same as above, for the most part you'll be fine.

You can BOOST your SEO rankings however if you're targeting specific regions or countries by hosting in that region or country and getting an IP for there. Google will boose the "Locale Search" or "Region Search" as a result.

Agreed. Page Rank will not suffer. And as Conor said, local IPs will help if you're targeting specific regions or countries. Search results will not be the same for the same query if searched from LA versus Miami versus London, and so on.

Thanks guys! So, PR will be passed, that's nice. But getting a country type domain in general can't be done if you're not a resident of that country, which is a problem for me because I have sites targeting various countries.

Depending on the country you're trying to get they have those regulations, however there are places that can register the name for you and place it under a privacy protection using their mailing address etc. It's not your NORMAL privacy protection, it's a service offered exclusively for people such as yourself that need a certain domain extension. Have a look on Google and you'll see a number of different services for this.

That is very good to know. I wasn't aware of that option before. It seems as a very practical and logical solution. I wonder does it costs more than regular services. I'll look into it, thanks!

as long as ur old hosting account is still on and u already migrate everything to ur new hosting account, the PR shouldn't be affect at all.

this is y so many people transferring away to new host b4 this old hosting account is cut off

For some bad experience i have to change Web Host 8 times in 3 months of a blog of mine (www dot sahityo dot com). And the result is:
It lost page rank 4 to 0.
It lost alexa rank 85623 to 125893

And also lost visitors as well.

IP have no meaning of ranking

Changing host has nothing to do with page rank .Follow the guide line of Google web master world ,you can easily get it from a new host.That is the reason many people prefer expired or old domains.

Changing in the server IP will not effect at all. But you should make sure that the server IP is not blocked and does not support any spamming site on the server.

http://www.netim.com/ provides such services for free and their registration fees are acceptable.