passing variable values to subsequent make calls

[Robert P. J. Day]

  what's the preferred way to pass some variable values to multiple
levels of recursive makes?

  i realize that, first, i can assign and export variables, as in

        export ARCH=ppc

and that variable will be available to all of my subsequent recursive 
makes.  but i've always been kind of leery of exporting variables at a top 
level of *anything* -- it reminds me too much of setting a global 
variable.

  if, in some makefile, i use

        ${MAKE} ARCH=ppc <subdir>

is it correct that that variable will only be visible just to that 
subdirectory make unless i explicitly set it again for further recursive 
calls?

  finally, i see in the make docs the construct:

        MAKE := ${MAKE} ARCH=ppc 

does this mean that, wherever i use the ${MAKE} invocation in any 
recursive makefile, that ARCH is automatically defined for all sub-makes 
all the way down?  i guess that's the way that would appeal to me the 
most, if that's how it works.

rday