Whatever equipment you provide to staff must be safe and comply with health and safety rules. Its electrical safety should be inspected periodically and employee workstations should be risk assessed to ensure that their use will not pose a threat to health.
Usually, employers will be liable to third parties for what their employees do using their equipment in connection with their employment. So if use is illegal, defamatory, discriminatory, breaches copyright or confidentiality, constitutes bullying or otherwise causes a legal problem, then the employer is on the hook.
Issues can arise in connection with inappropriate or excessive personal use of equipment. Where employees damage or lose equipment negligently, employers sometimes wish to deduct the cost from their pay; care must be taken to ensure this deduction is lawful.
Increasingly, employers want to examine and make use of information about employees use of IT equipment (eg by monitoring email and internet use), to take employment decisions. This raises issues of privacy and data protection as well as the fairness of disciplinary action.