Maybe I'm missing something here but this is very straight forward. IF you are saying the ltd company has 100 A class shares at £1 in your name and you want the other two newly appointed directors to own 10% each of the company then the simple answer is to issue 100 new shares in the company at £1 so your share capital becomes £200 (200 at £1) and of those new shares issue 60 to you and 20 each to both directors. They then own 10% each of the share capital and you are still the PSC with 80% control.
Now if it is you don't want them to have dividends or voting rights you could issue the 60 to you as A class with full voting and dividend rights and 40 B class to them and stipulate no dividend or voting rights on the B class shares.
Steps are these three filings at companies house:-
1. Resolution of allotment of securities: As the two others are directors already you need to pass a resolution confirming the proposed allotment of 100 new shares of £1 and the class and the split and all the directors each sign to pass the motion. You can attach the proposed shareholder schedule for the new shares.
2. Resolution: As you are the current 100% shareholder you need to sign a resolution confirming your agreement as shareholder to issue the new shares. Again you can attach the proposed shareholder schedule. Then issue the three new share certificates.
3. SH01 - Statement of capital following allotment of shares £200 - this form filed increasing your share capital to £200
You would then later need to file your updated
confirmation statement with the updated total shareholder list. i.e you 160 shares / person a 20 shares / person b 20 shares.
Of course you could use a solicitor to prepare your resolutions to file at companies house and the SH01 but to be honest i do all my own, its not difficult but if you are new to this and unsure then ask what they want to charge you, it not a big job.
Also, if you do above get each of you to pay the money from each for the shares into the business so that you have a record of the transaction. You don't want the revenue coming at your years down the line if you come to sell the stock and claiming the shares were gifted.
Finally, is a shareholder agreement, again if you are new to this use a solicitor. As
@WaveJumper jumper stated this is where you could have future disputes between the three of you but as you still have 80% control there is not a lot they can do IMO, with 80% you can practically pass whatever resolutions you like in the future.
If you don't want to use a solicitor message me and i can point you to some resolution wording filing examples. Hope my reply helps.
Good luck