I’ve downloaded the latest free version on my new net book. Do i have to register, although i may now want to keep it?
Yes you have to register it to use beyond the 30day trial.
From the avastUI, Maintenance, Registration section, complete the short form and you’re registered for a year, repeat the process after a year, still free.
If you have used Norton 30 day trial use the Norton removal tool & do a search for any Norton left over.
Since the OP says it’s a new netbook then most certainly the OP should remove any antivirus (it’s not limited to Norton, I’ve come across notebook pre-install with McAffee and Kaspersky) which came pre-installed by manufacturer whether the OP use the trial period or not.
I have found that the newer versions of Norton (since 2009 at least) uninstall very cleanly and do not require the use of the removal tool at all. Running it can’t hurt anything though. It actually wouldn’t even run on this machine and had to be shut down manually. A search of the system after just the regular uninstall routine and a registry clean by CCleaner found nothing that would cause any problems with any other security software.
I stopped using Norton in 2006 I thought it was a very good program & is still one of the top contenders.
Maybe it was too bloated back then but protected well.
You are right about Norton uninstalling but just as a precaution all traces of Norton or any other program should be fully removed.
Even after doing a uninstall & search, I bet Norton file is still in the registry whether it’s empty or not is another matter.
Norton used to do removal tools for their different products so maybe you tried the wrong removal tool, or maybe not, in safty mode is the way to go.
I suggested Norton on this guy’s computer because Norton is still one of the most popular with Mcaffee
They may be two of the most popular. Being the best choice is a whole other subject.
The reason these two (Norton and MacAfee) are pre-installed is due to contracts with the manufacturer. Which means the producer of the end product (computer) gets a cut whenever someone buys a subscription to the anti-virus software. Doesn’t make it right, it is how it is. 
A link worth looking at, which is a program removal tool that can remove the remnants of a number of different Norton Programs:
Removing your Norton program using SymNRT
Or ftp://ftp.symantec.com/public/english_us_canada/removal_tools/Norton_Removal_Tool.exe