PAYE employment + casual self-employment

[PattyPenguin]

I have an offspring who, in this tax year, has done a 3-month paid internship which has now ended, is looking for another placement or a job, but is in the meantime doing the odd day of work as a freelancer.

Do people in this position have to register as a sole trader while doing freelance work, then deregister when they get a job / paid placement with PAYE and NI deducted or when work dries up and they decide to register as unemployed? And repeat the exercise throughout the tax year?

He will have to do a self assessment tax return I believe. You don't have to deregister and register again if he takes on more work, as you can submit a self assessment return in addition to paying through PAYE. When you do the tax return you put down all the income and tax paid from your employed (PAYE) job (from your P60) and then you add in the self-employed work you have done and the tax payable is calculated for you.
The only issue is that they may request he submits a self assessment form every year from now on... however if all income for a tax year has gone through PAYE it is a very quick job to do once you have your P60s. I believe you can also make a declaration to HMRC that you do not need to do a self assessment anymore but whether that is more or less hassle than just doing it, I don't know!
(I have a PAYE job and also income through self employment and the odd ebay sale, so I do a self assessment every year. I'm not a tax expert though).

It's not as complicated as you think.

Just register as a sole trader, making sure you keep records of your turnover and outgoings.

Every year you complete a tax return online and as long as your turnover is under 84k you just tell them 2 figures, your turnover, and your outgoings to produce your "profit", which is taxable. You then give them details of any PAYE work you have completed during the same tax year and they use these to tell you how much tax you have to pay.

Honestly it's very simple.

There is no need to "de register" unless you give up the self employed work permenantly.

As moggle says, very simple.
Been simultaneously employed and self employed ( different part time roles) for years.

Just keep an eye on NI contributions: payments only count towards eg. pension if complete financial years , so make sure to look at whether you need to make contributions for any part of the year you're not employed, even if earning are low, and the contributions are voluntary.