JS Mill
Absolute freedom of the Press is about a publication being able to publish whatever they want, whenever they want. To be absolutely free, the Press has to be able to choose, without restraint, what to publish.
There is a problem with absolute freedom, however, because human needs and desires differ and so, inevitably, the strategies employed to satisfy them conflict. For example, a) may wish to work with the window open, while b) may wish to work with the window closed. More controversially a cartoon disrespecting a religious leader may be very witty and amusing to some, but extremely upsetting to others. In complex, multicultural societies harmony depends upon the co-operation between its citizens where the views of others are considered.  No man is an island and the actions of one person will affect another somewhere along the line.

So what should the press be prevented from printing? According to the 19th century moral philosopher John Stuart Mill, only views that harm others should be suppressed. For Mill, the causing of offence was not enough to justify censorship - harm has to be tangible. As Mill himself puts it:

“An opinion that corn dealers are starvers of the poor, or that private property is robbery, ought to be unmolested when simply circulated in the Press, but may incur punishment when delivered to an angry mob assembled before the house of a corn dealer.”

If there were general acceptance of Mill’s argument for the freedom of speech then the 21st century Press would possess considerable freedom to publish. Offence doesn’t, according to Mill, equate to harm. For example, in a society adopting Mill’s philosophy Salmon Rushdie’s book The Satanic Verses  would still have been published, even though it caused widespread offence to Muslims.

Nevertheless, if a direct causal link could be made between published material and harm to others then the reporting offensive material, under Mill’s “Harm Principle”, could be suppressed. Applying Mill’s principles in totality, then, the press is not free to publish absolutely anything. 

Today freedom of information is not dependent on the whim of an absolute Monarchy, as it was in the 17th century, but is threatened by a far more subtle force concealed in the form of ideologies. For example, The State Capitalism present in the Soviet Union in the mid 20th century, or the rapacious economic liberalism of the late 20th century. Both economic systems, in their own way, suppress information. The Soviets by openly banning all publications other than the State owned “Pravda” and in the West by engaging the press, as and when required, to rally around the State.
For example: In 1975 Britain held referendum asking its electorate to decided whether, or not Britain should remain part of the Common Market (The predecessor of the European Union). As Reported on the BBC's The Long View on the 16th October 2007 The Conservative Party, The Multinationals, The Confederation of British Industry argued for the YES campaign while The Trade Union Congress and The Labour Party argued that we should leave the Common Market. During this crucial campaign only The Spectator Magazine and the Morning Star came out in favour of the NO camp and the British public voted to stay within the Common Market.
One way or another, The State, wielding its ideological apparatus, is able to suppress and censor information as if it were a 17th century monarch desperate to keep information that would challenge its authority and position of privilege out of the public sphere.
Despite the mainstream press's bias in favour of free market capitalism impeding what is and what isn't published and the requirement for newspapers to consider libel and “public interest” laws deployed to censor the news, there is still potential for journalists to publish freely. As long as the 21st century press, in principle at least, embraces the idea of a free press, there is scope for the Press to negotiate the tyranny of a single dominant ideology and remain sufficiently free.
In absolute terms, however, because of the overriding power of dominant ideologies, the deployment of various censorship laws, coupled with the necessity to consider the harm to others caused by some published material, absolute freedom of the press is not currently possible.