My alyssum is doing the same, tumbling over the curb rather than on the lawn. I'm not sure what "Tiny Tim" is. A smaller form of alyssum? I would think you would at least wish to clip it back from the lawn because it will eventually kill the lawn it covers.

A perennial 4-6" high would be a ground cover. I've had good luck with thyme, but mine doesn't bloom like alyssum does. There are some succulent ground covers which are nice, but if the sprinklers hit there, it could be a little too wet. Mexican heather is a taller but makes a nice border. I cant think of the Latin name now.

If you don’t like it, I’d pull it out before it reseeds. It can be hard to get rid of.

Oh yes it reseeds readily, I'll agree with that, socalgal, and probably it's too late to prevent that. But I've not found it hard to get rid of, just a scuff of the foot or a hoe for a while.

Hi im a new gardner is it ok to pant Alyssum & blue Flax seed in the ground today Dec 5, im in zone 9

I’m in zone 10 and still have some volunteer sprouts of alyssum. why not try it? Don’t use all your seeds, save some for spring in case you are not happy with fall seeding.