This paper poses a few fundamental questions regarding the attributes of the volume profile of a Limit Order Books stochastic structure by taking into consideration aspects of intraday and interday statistical features, the impact of different exchange features and the impact of market participants in different asset sectors. This paper aims to address the following questions: 1. Is there statistical evidence that heavy-tailed sub-exponential volume profiles occur at different levels of the Limit Order Book on the bid and ask and if so does this happen on intra or interday time scales ? 2.In futures exchanges, are heavy tail features exchange (CBOT, CME, EUREX, SGX and COMEX) or asset class (government bonds, equities and precious metals) dependent and do they happen on ultra-high (<1sec) or mid-range (1sec -10min) high frequency data? 3.Does the presence of stochastic heavy-tailed volume profile features evolve in a manner that would inform or be indicative of market participant behaviors, such as high frequency algorithmic trading, quote stuffing and price discovery intra-daily? 4. Is there statistical evidence for a need to consider dynamic behavior of the parameters of models for Limit Order Book volume profiles on an intra-daily time scale ? Progress on aspects of each question is obtained via statistically rigorous results to verify the empirical findings for an unprecedentedly large set of futures market LOB data. The data comprises several exchanges, several futures asset classes and all trading days of 2010, using market depth (Type II) order book data to 5 levels on the bid and ask.