A series of articles should be published all in the same journal, or in different journals? There is a series of papers, which build on each other, to be published. The series starts with purely mathematical articles, and ends with articles oriented to some applications. What would be the best approach:


*

*Submit all to the same journal. If so, what kind of journal would be best, a purely mathematical one, one of applications, or something between?

*Submit them to different journals, possible ranging as well from pure mathematics to applied mathematics.

*Try to make two series, one purely mathematical, and the other oriented towards applications, and send them to two journals.

*Other solution.
What advantages and disadvantages has each solution?
 A: If the result is good  and  the level of journals  is high, 
I would submit to different journals. There is no disadvantage to the reader (especially if you put the papers in arXive);  no silly question of the form "may be the author has good relations with somebody in the editorial body" will appear, and IMHO   the chances for acceptance are higher.  
Making two series of papers would require a lot of additional work (and that's why  I would not do it) but is also admissible .  
A: Point 2. seems best to me. Treat each paper as an individual one and choose the journal accordingly. However, make sure that the other papers are available (for example on the arXiv) in order to make the reviewers and editors life easier.
Also, mention in each introduction the 'structure' of the series; of course, not in a too lengthy way.
It is also not unusual to distribute a series over several journals.
Point 1. seems like a good idea in theory, but is in my opinion/experience 'risky.'
The only advantage I can see is that the editor and the reviewer might be better aware of the strcuture of the series. However, I definitely would not count on the editor choosing the same reviewer for each of the articles. Better, include in each instroduction a brief explanation and make the other papers easily available (as said above).
Even for a thematically very homogenous series, so that all articles could appear well in one and the same journal, I do not think they should all be submitted to the same journal (for various reasons; but this is a different question). So I see little reason to do 3.
Regarding other options: to answer this one would need a bit more information. In principle, one could write one very long paper, or even a book, or something in between (Memoirs of the AMS, Asterisque). However, in practice this could be difficult, in particular if you are at the beginning of your career, and whether or not this is a good idea also depends on the academic system. 
A: I would like to second Steve Gubkin's point.  While it is not as good for your paper count, publishing things together as a single item is not only kind to the reader, it also places your work where it is more likely to be read, or at least cited.  I remember a conversation long ago with John Ewing, then Executive Director of the AMS.  He told me of everyone's surprise, after the introduction of the Citations addition to Math Reviews, that books were (and I'm sure still are) cited far more often than articles, way more than one would guess by perceived quality.  Books include things like Memoirs of the AMS and Asterisque volumes, for example.
A: I think Gian-Carlo Rota's famous series of papers titled "Foundations of Combinatorial Theory I", "Foundations of Combinatorial Theory II", etc. through about X, appeared in various different journals.
A: 1.) I know the consensus here seems to be to publish in different journals, I will just give a famous example for the mix in which the series of articles were all published in the same journal.  Not only that, but Part II and Part III were even published in the same issue of that journal.
J Cheeger and T Colding (1997) On the structure of spaces with Ricci curvature bounded below I.  J. Diff. Geom., 45: 406-480.
J Cheeger and T Colding (2000) On the structure of spaces with Ricci curvature bounded below II.  J. Diff. Geom., 54: 13-35.
J Cheeger and T Colding (2000) On the structure of spaces with Ricci curvature bounded below III.  J. Diff. Geom., 54: 37-74.
2.) Another example in theoretical physics is given by the series of two papers by Dine, Seiberg, Wen and Witten on nonperturbative effects on the string world sheet. The two papers were originally published in the same journal: Part I and Part II.
3.) Sturm published Part I and Part II of his two-part series of articles on the geometry of metric measure spaces in the same issue of the same journal.
4.) Yet another example on the engineering side, I just saw a series of two papers on waves and turbulence modelling, both published in the same journal: Part I - Formulation and Part II - Applications.
5.) Famous example from topology:
Hopf H., ''Abbildungsklassen $n$-dimensionaler Mannigfaltigkeiten'', Math. Annalen 96 (1926), 209-224.
Hopf H., ''Vektorfelder in $n$-dimensionalen Mannigfaltigkeiten'', Math/ Annalen 96 (1926), 225-250.
So it hardly seems unusual to publish a series of papers in the same journal, even when the final article in the series is different to the others and focussed on applications.
A: An old question, but an interesting example is Robertson & Seymour’s monumental series of papers Graph Minors I, Graph Minors II, Graph Minors III and so on up to Graph Minors XXIII.
All published in Journal of Combinatorial Theory, Series B EXCEPT for Graph Minors II, which was in Journal of Algorithms.
I guess we can count that as a vote for the “all in one journal” option.
A: Both as an author but also as a referee I made the experience that journals are usually not very happy to have series of papers. In particular, if it is not really clear whether part 56 still has some significant new content or if it is just incremental. I have been asked to check manuscripts precisely for that and decline them if so (on request by by some journals...)
In some sense, I can also understand this attitude: for a possible reader it is very discouraging if s/he gets part 33 into his/her hands and if s/he has the impression that s/he has to go through part 1-32, too, just to understand a little lemma in part 33. This is of course an extreme, but usually people are happy if they can read a rather short paper which has a single clear result. Of course, 99% of the papers will build on some previous resources, but I think it is a good idea to write papers rather self-contained: at least, I've been told by many people that they personally would prefer this.
Now to your problem, which is not at all unfamiliar to me ;) If you have a long string of thought, ranging from some pure/theoretical foundations to some applied examples, things become tricky. There might be no good solution, but I think even in this case, it might be good to split things into parts which can be read rather independently of each other. Then there is no need to call part 55 part 55 but it will be a separate paper which can be submitted to the optimal journal for this piece of math. Privately, you can still call it part 55 ;)
What might be an option is that after the whole project has been published in variuos journals: write a good review of it. I think, for long (over many years) projects it will become increasingly important to have good reviews by people really working in this field. Then a reader can decide whether s/he will really have to take a look at all relevant parts (papers) or just at a few ones. Of course, producing a good review is not at all an easy task, it is much more than just cut-copy-paste some pieces of previous research articles.
Hmmm, I think I have not really answered the question, but I gues what I said matches perhaps best to your point 2.). However, I really would avoid to call the title of the paper Theory XY, part IIX...
A: I have been told by a senior mathematician who is in the course of publishing a long series of papers (4 to date, each of at least 40 pages, all in excellent journals) that the journal which accepted his first paper rejected the second one on the grounds that, regardless of merit, they could not spend so many pages on similar topics. 
I'd be very interested to hear comments from journal editors as to whether this is common.
A: The real question to ask is why you make it a series of papers rather than just one paper. If you see a clear logical separation between parts and each part is devoted to something different and/or intended for a different audience, then the division is justified and the choice of the journal should be made independently for each part (independent variables do not need to be pairwise distinct, of course). In all other cases, you should really think of why you split the way you do and tell that reason. I doubt it is possible to give a good advice without knowing the answer to this question.
Another general suggestion is to put them all on ArXiV and do full cross-referencing so that the readers of part 3 will be able to find part 1 if needed. If you just submit different parts of the series to different journals, it is possible that part 3 will appear a year before part 1 or, even worse, that part 3 will be published and part 1 will be rejected, which would result in quite a mess from the reader's perspective.
