As one delves into the intricate world of business operations, the importance of an efficient helpdesk cannot be overstated. An operational cornerstone and a transactional hub, the helpdesk serves as a nexus between the company and its customers. As businesses expand and complexities mount, many are opting to outsource their helpdesk functions to third-party providers. This decision, however, necessitates a meticulous understanding of the outsourced helpdesk's workings and their alignment with the company's objectives. Therefore, it is crucial to ask pertinent questions before choosing a helpdesk outsourcing company.

One needs to first comprehend the raison d’être of outsourcing. The premise of the transaction cost theory, as posited by economist Ronald Coase, suggests that companies will externalize operations if the cost of performing them in-house exceeds the cost of outsourcing. While the savings derived from economies of scale, specialization, and global labor arbitrage are compelling, one must balance them against the potential risks, including loss of control, quality issues, and the possibility of opportunistic behavior by vendors.

The first question to ask pertains to the nature of the provider's technological capabilities. Do they employ advanced tools such as artificial intelligence (AI) and machine learning (ML) for handling customer queries? A helpdesk powered by AI can automate responses to frequently asked questions, using machine learning to improve its accuracy over time. However, the human element should not be forgotten as AI can sometimes fail to understand the nuances of human communication. Therefore, an ideal provider balances AI and human intervention.

Next, query about the provider's expertise in your industry. Just as Alfred Marshall's principle of agglomeration stresses on the importance of industry-specific knowledge clusters, a helpdesk provider with prior experience in your industry brings a wealth of relevant insights and acumen. They would be more adept at understanding your customers and your product or service, which could translate into better customer satisfaction.

Thirdly, delve into their security protocols. As per the general deterrence theory in criminology, a potent defense mechanism can act as a powerful deterrent against potential wrongdoers. Similarly, robust cybersecurity protocols, including encryption and two-factor authentication, can deter cybercriminals from breaching the helpdesk's data, which often includes sensitive customer information.

Fourthly, the provider's approach towards metrics and KPIs warrants scrutiny. An effective helpdesk provider should not only measure typical KPIs like first response time and resolution time, but also dig deeper into metrics like customer satisfaction, agent performance, and the overall impact of their service on your business. This reflects the influence of the Balanced Scorecard Approach, which asserts that organizations should evaluate performance from multiple perspectives for a more holistic understanding.

Lastly, consider the flexibility of the provider. The punctuated equilibrium theory from evolutionary biology, which proposes that species evolve during short, rapid bursts of change, could be analogous to the business environment. Amid this fast-paced evolution, a helpdesk provider must be flexible enough to adapt to sudden changes in volume or complexity of customer queries.

In conclusion, choosing a helpdesk outsourcing company is a significant decision that requires a comprehensive evaluation. It involves sifting through the provider's technological prowess, industry expertise, security measures, performance metrics, and adaptability. By asking these questions, businesses can ensure they select a partner that aligns with their goals and amplifies their customer service efforts. It's a process that is both an art and a science, a delicate dance between robust empirical analysis and intuitive judgement.