Blockchain, a technology that rose to prominence with the advent of cryptocurrencies, particularly Bitcoin, has since found its applications seeping into multifarious industries. The consulting services built around blockchain technology have also grown in leaps and bounds, carving a niche for themselves in the digital transformation landscape. It is therefore incumbent upon us to explore the future trajectory of this burgeoning sector, extrapolate its emerging trends, and make certain calculated predictions.

The underpinning feature of blockchain technology is its decentralized nature. It operates on a distributed ledger system, devoid of a central authority, thereby ensuring transparency and security in transactions. This attribute is a game-changer for various industries, particularly finance and supply-chain, which depend heavily on trust and authenticity.

In a unique blend of technology and consulting, blockchain consulting services have emerged to assist companies in leveraging this nascent technology effectively. These services primarily focus on providing strategic advice regarding blockchain's applicability, integration, and management, along with operational support for blockchain-enabled systems.

The growth of blockchain consulting services can be primarily attributed to two factors. Firstly, the demand for blockchain solutions is escalating, as more and more businesses across diverse sectors realize the potential of this technology. Secondly, the complexity and novelty of blockchain technology make it less accessible to many organizations, necessitating expert consulting to unveil its true potential.

Now, let us foretell the future of this sector, through the lens of historical precedents, mathematical probabilities, and evolving market trends. The first prediction is that the demand for blockchain consulting services will continue to grow exponentially. According to a report by Markets and Markets, the global blockchain market size is expected to expand from USD 3.0 billion in 2020 to USD 39.7 billion by 2025, at an impressive Compound Annual Growth Rate (CAGR) of 67.3% during 2020–2025. This growth will undeniably create vast opportunities for blockchain consulting services.

The second prediction pertains to the diversification of services. As blockchain technology evolves and matures, consulting services will also need to expand their spectrum, moving beyond just strategic advice to more specialized areas. These might include legal consulting for blockchain-related regulations, technical consulting for blockchain integration and troubleshooting, and even ethical consulting given the potential misuse of this technology.

Drawing upon the principles of economics, we could also anticipate a surge in competition within the blockchain consulting sector. As the potential profitability of this sector becomes more apparent, it might attract more players, leading to a more competitive market. This could in turn foster innovation and improvement in service quality.

Finally, we may also expect some degree of consolidation in the market as competition intensifies. Larger consulting firms might acquire smaller niche players to gain a competitive edge and capture a larger market share.

Emerging trends in this sphere also warrant our attention. Given the inherent link between blockchain and cryptocurrencies, we can expect blockchain consulting services to play a pivotal role in the development of Central Bank Digital Currencies (CBDCs). As more countries explore the possibility of launching their own digital currencies, the expertise of blockchain consultants will be crucial.

Another trend to watch out for is the integration of blockchain with other cutting-edge technologies, such as Artificial Intelligence (AI) and Internet of Things (IoT). The convergence of these technologies could create a myriad of opportunities for blockchain consulting services.

In conclusion, whilst acknowledging the speculative nature of these predictions, one thing is certain - the future of blockchain consulting services looks promising. Drawing upon historical precedents, mathematics, economics, and market trends, we can confidently state that the sector is poised for growth, diversification, and competition. Riding the wave of digital transformation, blockchain consulting services are set to transform the way we do business, making them an indispensable part of the future corporate landscape.