Ever since the web began, the number of websites has been growing exponentially. These websites cover an ever-increasing range of online services that fill a variety of social and economic functions across a growing range of industries. Yet the networked nature of the web, combined with the economics of preferential attachment, increasing returns and global trade, suggest that over the long run a small number of competitive giants are likely to dominate each functional market segment, such as search, retail and social media. Here we perform a large scale longitudinal study to quantify the distribution of attention given in the online environment to competing organisations. In two large online social media datasets, containing more than 10 billion posts and spanning more than a decade, we tally the volume of external links posted towards the organisations' main domain name as a proxy for the online attention they receive. We also use the Common Crawl dataset -- which contains the linkage patterns between more than a billion different websites -- to study the patterns of link concentration over the past three years across the entire web. Lastly, we showcase the linking between economic, financial and market data by exploring the relationships between online attention on social media and the growth in enterprise value in the electric carmaker Tesla. Our analysis shows that despite the fact that we observe consistent growth in all the macro indicators -- the total amount of online attention, in the number of organisations with an online presence, and in the functions they perform -- we also observe that a smaller number of organisations account for an ever-increasing proportion of total user attention, usually with one large player dominating each function. These results highlight how evolution of the online economy involves innovation, diversity, and then competitive dominance.