Parallel Fluorescent Wiring
What do you want to connect in parallel?

The Live and Neutral? 

That is the correct way to do it.

Each 'L','N' must be connected to each next 'L','N' in parallel from your main power source. Also it is a good idea to earth all your florescent lights to a earth leakage breaker or something similar as they can sometimes develop high voltage leaks and cause undesired effects..(smoke/fire,etc)

Do not exceed by 1200Watts on a 5AMP Breaker in 240Volts

You cannot connect the florescent tubes in parallel or in fact any other way than the ballast was designed to handle it. You can get double/triple ballasts too and the internal wiring can get somewhat 'spaghetti' like. 

Each tube needs to be handled by 1 ballast as it 'starts' the tube then 'sustains' the voltage for it.

There are new electronic ballasts that do not require starter caps and 'start' the tubes quicker with less stress extending the life of the tube up to 25%.