People have often set up limited companies and VAT registered them, so they could reclaim the purchase VAT on the aircraft. For any reasonably decent plane, this is a massive amount of money recovered e.g. £35,000 on a new TB20. But it was a stupid approach, because all renters (including you the owner) then need to be invoiced at the rate "plus VAT" and this continues for ever...
Not at all stupid, because VAT can then be reclaimed on all fuel purchases, maintenance etc , also a massive amount of money.