While trying to debug some of my batch apex, i'm noticing that batches can run in parallel, whereas I used to think they always ran in sequence.

I have a batch job, that ends up consisting of 4 batches, i.e. 4 calls of execute().  Let's call the batches A, B, C, and D.  Their times of execution are noted below.

A runs from 14:51:16.017 to 14:51:16.067
B runs from 14:51:17.019 to 14:51:17.148
C runs from 14:51:17.019 to 14:51:17.108
D runs from 14:51:17.022 to 14:51:17.259

 These times are taken from debug logs, and you can see that B, C, and D run in parallel.

I was under the impression that these batches run serially.  Infact, the following post says that as well:

Filed a Case to ask this question, and got this response from Tech Support:
 
1. Is it possible for the execute() method to be running more than once at the same time? (I've already confirmed that the batch job was launched only once.)

A:
All execute methods for batches within a batch job are synchronous so they will not "trip" over each other.

[posted at: http://boards.developerforce.com/t5/Apex-Code-Development/Batch-Apex-can-execute-invocations-run-concurrently/m-p/261857#M45628]

I'm hoping that this is true, that somehow you can have the batches run in sequence, but my experience above says otherwise.  Aftering performing timings with Database.stateful, I see that has no effect on the parallel execution of execute().

Anyone have any input on this topic?  Should I rewrite my batch job so that batches are not dependent of other batches?  Ideally, i'd like the batches to execute sequentially.