Most likely you would have a small cherry type tomato.Hybrids tend to revert back to the species or wild tomato.There is a very slim chance that you would get a decent tomato,hoever I doubt that it would be improved.

MY NEIGHBOR used to save the seeds from his best " better boy " tomatoes one year the bees crossed them with the : golden marglobe, resulting in a large yellow strain, fantastic, resulting in a large pointed strain, ponderosa resulting in an even larger light red purple (oxheart strain).these were the F1 generation . the neighbor was not pleased but I considered them an interesting improvement.
Try it see what you get . you will never know unless you try . What have you got to lose ? i noticed in the previous case all the tomatoes had the size of the female type "Better boy" they all tasted good. you can always eat your mistakes.

I would surmise then that the name "Early Girl' has not been patented. Originally was an indeterminate hybred. Now you can buy seeds for Early Girl bush, determinate. So they don't bear any relationship?

Most plant names are not patented, they are simply registered with a breed society. It is better, for the sake of confusion, not to use the same name again, but if you produce a variety that you intend to sell commercially, you can call it whatever you like, so long as the name is not covered by plant breeders rights, or is a name that might land you in court. (The 'Harry Potter' tomatoe, for example)
King Alfred daffodils are a good example of a name that has been misused for many years, as it has been used to describe anything that looks remotely like the original KA's.
Cheers, Jan

Even if you just saved seed from Early Girl, you would not have Early Girl, because it is a hybrid. You would have F2 seed which will (if you grow out enough) display all the possible combinations of traits of the parents of Early Girl. (Contrary to an earlier response, it won't revert back to a wild form.)

Crossing it with yet another type of tomato will add even more variability to the mix.

If you've got plenty of space to grow out the progeny, you can then save seed from the best plant and grow them the next year. Repeating this for several generations will eventually stabilize the line, because each year a plant self-crosses, it stabilizes about half of the remaining heterozygous genes.

And when you've got a stable line, you can call it Open Pollinated Improved Early Girl (or whatever you want to call it) and introduce it to the world.

The seedlings grown from seed of a selfed F1 plant are never uniform in type. You will get a lot of variation. The F1 has pairs of non identical chromosomes because it comes from a cross between 2 selected homozygous strains of tomato (AA,BB,CC etc crossed with aa,bb,cc, etc where A and a are two unlike chromosomes) It is not a 'hybrid' but a 'First Cross' (F1) of 2 selected strains.
So the F1 generation of seedlings will be almost identical depending on how homozygous the parent plants are, and allowing for some crossing over of genes during meiosis. The F1 seedlings will all have a chromosome set of: Aa, Bb, Cc, etc, but their offspring will be well mixed (AA or Aa or aa),(BB or Bb or bb),(CC or Cc or cc)
You can see that the number of different types of chromosome combinations will be roughly 3x3x3x3x3 etc (how many pairs does a tomato plant have?)
If you get a few plants that you like, and keep seed from these, you will still not get a consistant type, but if you select and line breed (in breed) for several generations you start to again approach a homozygous type (AA, BB, CC, etc) (or aa,bb,cc).
If you out cross to another tomato - the number of possible chromosome combinations becomes even greater, as you bring in more genetic traits.
Hope that is clearer than mud :-)
Cheers, Jan

What are the PARENT PLANTS of the Early Girl Hybrid?? Does anyone know or know where to search?