I'm still not sure what Paul Z is getting at, but I'll take another 
bite as promised.
-------------
"The employment of surplus-value as capital, or its reconversion into 
capital, is called accumulation of capital" (Volume 1, Penguin ed., p. 725).
-------------
That's the definition that Marx gives in the first paragraph of Ch. 24 
("The Transformation of Surplus-Value into Capital").
As such, the accumulation of capital is not the mode of production, 
capitalism, but a dynamic that *typically* goes on under capitalism.
In the context of "capital in general" in Volume 1, according to Mandel 
"he [Marx] examines it essentially in the light of what occurs and flows 
from the exchange between wage-labour and capital. In Volume 3, he 
examines capital accumulation (economic growth under capitalism) in the 
light of what occurs in the sphere of 'many capitals', that is of 
capitalist competition." (Ibid, p. 62)
[Note the less precise definition given by Mandel above. Also note that 
the meaning of 'many capitals' *as* capitalist competition implies 
something regarding the *form* that competition takes at that level of 
analysis.]
On p. 36, Mandel gives the even more vague definition of ""The 
accumulation of capital, i.e. capitalist wealth in its totality ...."
So, before proceeding further, I would have to *agree* with Paul Z. when he 
says that "accumulation of capital" is frequently used imprecisely. 
Additional comments:
(1) Note that the subject of the process of accumulation of capital is 
first introduced in V1 *following* Marx's first discussion of simple 
reproduction in Ch. 23. This should make it clear that the development of 
this subject is tied to the analysis of extended reproduction. The 
discussion moves next to Ch. 25 ("The General Law of Capitalist 
Accumulation"). Particularly relevant, in would seem, are Sections 2-4.
(2) Interestingly, Mandel did not refer to Volume 2 in the quote above. 
Yet, don't many topics in Volume 2 relate to the accumulation of capital? 
Indeed, don't Parts 1-3 all refer, in part, to this process? For example, 
Part One, Ch. 5, Sections 2-4; Part Two, Ch. 17, Section 2; Part Three, 
Ch. 21. Ch. 21, it would seem, has particular relevance for understanding 
Marx's conceptions regarding the *possibility* of both accumulation of 
capital and capitalist crisis.
(3) The subject then of the accumulation of capital would seem to be tied 
to Marx's attempt to lay bare the "law of motion of modern society." One 
part of Marx's project would seem to be the explanation of the process 
that *lies behind* the accumulation of capital. That is, classical 
political economy and the physiocrats, for instance, were able to 
comprehend the *appearance* of accumulation but not its *source* and the 
dynamic that lies behind this process. This would suggest that the 
process of the accumulation of capital has to be developed logically by 
first explaining the commodity, value, surplus value, capital, etc. -- 
complete with all of the "Hegelianisms" in the first part of V. 1. 
(That's a comment that is sure to get a response from Paul Z). 
(4) In addition to explaining the source and force behind the 
accumulation of capital, Marx also, by my reading, wants to explain the 
contradictory nature of the accumulation process. This is, again by my 
reading, part of Marx's undertaking in Volume 3, Chapters 13-15 and many 
subsequent chapters.
(5) What interests me, though, is how the accumulation of capital is 
affected by such questions as:
    * relations with pre-capitalist social formations and landed property;
    * the accumulation of workers and the self-activity of the working class;
    * the accumulation of use values and the creation of needs;
    * foreign trade;
    * the state;
    * the world market and crisis.
Until we have examined all of the above questions, and other relevant 
ones, how can we say that we understand the accumulation of capital 
(in its more developed forms) under capitalism?
OK, I did my bit (bite) (bytes). Who's next?
In OPE-L Solidarity,
Jerry