“Challenge the mind and capture the heart,” was Carly Fiorina’s management mantra, according to the Fortune magazine article published in 2000 that named her, for the second year running, as the most powerful female CEO in America.

In February, after five and a half years at the helm of IT giant Hewlett-Packard (HP), Fiorina lost that power, with hearts and minds the key issue: in spite of a respectable financial performance over the past year, it was Fiorina’s failure to maintain the support of her investors that led to her downfall.

Now customers and business partners are waiting to see how the change of leadership affects them. A new leader could dramatically change the size, shape and focus of HP.

Fiorina’s defining act was the $19 billion takeover of rival Compaq, justified on the grounds of increased shareholder value and her belief that only the biggest companies could profitably survive. Critics, and possibly some board members, have argued that the printer unit alone is worth as much as the whole of HP. In that case, they argued, why not sell it, leaving HP with tens of billions in cash, and a valuation that can only go up? Some even argue the PC business should be sold.

Clear parallels can be seen with IBM and its crisis in the early 1990s. CEO John Akers was forced out because of dire performance – and investors pushed for a break of IBM into valuable units. The new CEO, Louis Gerstner, however, proved to be a centralist, and built IBM into a company with tight integration, led by its services arm.

It was this strategy that Fiorina wanted, but struggled to follow. Fiorina recently said she passed over on eight opportunities to buy the PwC services business, which IBM eventually bought and used to sell both services and IBM products. The question for HP’s new leader: To try again, with a lot more cross selling and service, or break up the company?