When does it make sense to vertically integrate or disintegrate?

In a famous 1951 paper, Nobel Laureate George Stigler argued that “vertical disintegration is the typical development in growing industries, vertical integration in declining industries” (George Stigler, The division of labor is limited by the extent of the market, Journal of Political Economy 59, June 1951: 185-193)

From Invisible Engines: How Software Platforms Drive Innovation and Transform Industries (page 260):

Stigler noted that at the inception of new industries, vertical integration is necessary because the technologies involved are unfamiliar. It is therefore hard for firms to persuade outsiders to participate in a business with uncertain prospects and with which they have had little or no experience. If and when the industry grows and becomes viable, many of the tasks involved in the production processes are sufficiently well defined and are performed on a sufficient scale to make it possible for an integrate early entrant to turn them over to specialized firms, either as suppliers or as complementors. It is also profitable to do so provided the market of specialists is sufficiently competitive. Disintegration frees previously integrated firms to concentrate on those parts of the final product on which they have a comparative advantage.
 

Christensen in the The Innovator’s Solution(page 134) describes the process of modularization and disintegration as a predictable casual sequence made of:

1. The pace of technological improvement outstrips the ability of customers to utilize it, so that a product´s functionality and reliability that were not good enough at one point overshoot what customers can utilize at a later point
2. This forces companies to compete differently: The basis of competition changes. As customers become less and less willing to reward further improvements in functionality and reliability with premium prices, those suppliers that get better and better at conveniently giving customers exactly what they want when they need it are able to to earn attractive margins.
3. As competitive pressures force companies to be as fast and responsive as possible, they solve this problem by evolving the architecture of their products from being proprietary and interdependent toward being modular
4. Modularity enables the dis-integration of the industry. A population of non integrated firms can now out compete the integrated firms that had dominated the industry. Whereas integration at one point was a competitive necessity, it later becomes a competitive disadvantage.