You must declare your earnings as that of a sole trader business (under your own name) and then declare the computer as a capital allowance in that section.
Like a sole trader, partners will be liable on any contract or tort obligation jointly and severally in shares equal to their monetary contribution, or according to their culpability.
The amendments to the capital allowance regime are an added incentive to business operators, whether they are operating as a company, sole trader or in partnership.
