size_t is defined by the C standard to be the unsigned integer return type of the sizeof operator (C99 6.3.5.4.4), and the argument of malloc and friends (C99 7.20.3.3 etc). The actual range is set such that the maximum (SIZE_MAX) is at least 65535 (C99 7.18.3.2).
However, this doesn't let us determine sizeof(size_t). The implementation is free to use any representation it likes for size_t - so there is no upper bound on size - and the implementation is also free to define a byte as 16-bits, in which case size_t can be equivalent to unsigned char.
Putting that aside, however, in general you'll have 32-bit size_t on 32-bit programs, and 64-bit on 64-bit programs, regardless of the data model. Generally the data model only affects static data; for example, in GCC:
`-mcmodel=small'
Generate code for the small code model: the program and its
symbols must be linked in the lower 2 GB of the address space.
Pointers are 64 bits. Programs can be statically or dynamically
linked. This is the default code model.
`-mcmodel=kernel'
Generate code for the kernel code model. The kernel runs in the
negative 2 GB of the address space. This model has to be used for
Linux kernel code.
`-mcmodel=medium'
Generate code for the medium model: The program is linked in the
lower 2 GB of the address space but symbols can be located
anywhere in the address space. Programs can be statically or
dynamically linked, but building of shared libraries are not
supported with the medium model.
`-mcmodel=large'
Generate code for the large model: This model makes no assumptions
about addresses and sizes of sections.
You'll note that pointers are 64-bit in all cases; and there's little point to having 64-bit pointers but not 64-bit sizes, after all.